Smith numbers: Difference between revisions
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<pre>[4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]</pre> |
<pre>[4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]</pre> |
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=={{header|Mathematica}}== |
=={{header|Mathematica}}/{{header|Wolfram Language}}== |
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<lang Mathematica>smithQ[n_] := Not[PrimeQ[n]] && |
<lang Mathematica>smithQ[n_] := Not[PrimeQ[n]] && |
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Total[IntegerDigits[n]] == Total[IntegerDigits /@ Flatten[ConstantArray @@@ FactorInteger[n]],2]; |
Total[IntegerDigits[n]] == Total[IntegerDigits /@ Flatten[ConstantArray @@@ FactorInteger[n]],2]; |
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Select[Range[2, 10000], smithQ]</lang> |
Select[Range[2, 10000], smithQ]</lang> |
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Revision as of 23:15, 14 August 2021
You are encouraged to solve this task according to the task description, using any language you may know.
Smith numbers are numbers such that the sum of the decimal digits of the integers that make up that number is the same as the sum of the decimal digits of its prime factors excluding 1.
By definition, all primes are excluded as they (naturally) satisfy this condition!
Smith numbers are also known as joke numbers.
- Example
Using the number 166
Find the prime factors of 166 which are: 2 x 83
Then, take those two prime factors and sum all their decimal digits: 2 + 8 + 3 which is 13
Then, take the decimal digits of 166 and add their decimal digits: 1 + 6 + 6 which is 13
Therefore, the number 166 is a Smith number.
- Task
Write a program to find all Smith numbers below 10000.
- See also
- from Wikipedia: [Smith number].
- from MathWorld: [Smith number].
- from OEIS A6753: [OEIS sequence A6753].
- from OEIS A104170: [Number of Smith numbers below 10^n].
- from The Prime pages: [Smith numbers].
11l
<lang 11l>F factors(=n)
[Int] rt
V f = 2
I n == 1
rt.append(1)
E
L
I 0 == (n % f)
rt.append(f)
n I/= f
I n == 1
R rt
E
f++
R rt
F sum_digits(=n)
V sum = 0
L n > 0
V m = n % 10
sum += m
n -= m
n I/= 10
R sum
F add_all_digits(lst)
V sum = 0
L(i) 0 .< lst.len
sum += sum_digits(lst[i])
R sum
F list_smith_numbers(cnt)
[Int] r
L(i) 4 .< cnt
V fac = factors(i)
I fac.len > 1
I sum_digits(i) == add_all_digits(fac)
r.append(i)
R r
V sn = list_smith_numbers(10'000) print(‘Count of Smith Numbers below 10k: ’sn.len) print() print(‘First 15 Smith Numbers:’) print_elements(sn[0.<15]) print() print(‘Last 12 Smith Numbers below 10000:’) print_elements(sn[(len)-12..])</lang>
- Output:
Count of Smith Numbers below 10k: 376 First 15 Smith Numbers: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 Last 12 Smith Numbers below 10000: 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
360 Assembly
<lang 360asm>* Smith numbers - 02/05/2017 SMITHNUM CSECT
USING SMITHNUM,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R10,PG pgi=0
LA R6,4 i=4
DO WHILE=(C,R6,LE,N) do i=4 to n
LR R1,R6 i
BAL R14,SUMD call sumd(i)
ST R0,SS ss=sumd(i)
LR R1,R6 i
BAL R14,SUMFACTR call sumfactr(i)
IF C,R0,EQ,SS THEN if sumd(i)=sumfactr(i) then
L R2,NN nn
LA R2,1(R2) nn+1
ST R2,NN nn=nn+1
XDECO R6,XDEC i
MVC 0(5,R10),XDEC+7 output i
LA R10,5(R10) pgi+=5
L R4,IPG ipg
LA R4,1(R4) ipg+1
ST R4,IPG ipg=ipg+1
IF C,R4,EQ,=F'16' THEN if ipg=16 then
XPRNT PG,80 print buffer
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi=0
MVC IPG,=F'0' ipg=0
ENDIF , endif
ENDIF , endif
LA R6,1(R6) i++
ENDDO , enddo i
L R4,IPG ipg
IF LTR,R4,NZ,R4 THEN if ipg<>0 then
XPRNT PG,80 print buffer
ENDIF , endif
L R1,NN nn
XDECO R1,XDEC edit nn
MVC PGT(4),XDEC+8 output nn
L R1,N n
XDECO R1,XDEC edit n
MVC PGT+28(5),XDEC+7 output n
XPRNT PGT,80 print
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
- ------- ---- ----------------------------------------
SUMD EQU * sumd(x)
SR R0,R0 s=0
DO WHILE=(LTR,R1,NZ,R1) do while x<>0
LR R2,R1 x
SRDA R2,32 ~
D R2,=F'10' x/10
LR R1,R3 x=x/10
AR R0,R2 s=s+x//10
ENDDO , enddo while
BR R14 return s
- ------- ---- ----------------------------------------
SUMFACTR EQU * sumfactr(z)
ST R14,SAVER14 store r14
ST R1,ZZ z
SR R8,R8 m=0
SR R9,R9 f=0
L R4,ZZ z
SRDA R4,32 ~
D R4,=F'2' z/2
DO WHILE=(LTR,R4,Z,R4) do while z//2=0
LA R8,2(R8) m=m+2
LA R9,1(R9) f=f+1
L R5,ZZ z
SRA R5,1 z/2
ST R5,ZZ z=z/2
LA R4,0 z
D R4,=F'2' z/2
ENDDO , enddo while
L R4,ZZ z
SRDA R4,32 ~
D R4,=F'3' z/3
DO WHILE=(LTR,R4,Z,R4) do while z//3=0
LA R8,3(R8) m=m+3
LA R9,1(R9) f=f+1
L R4,ZZ z
SRDA R4,32 ~
D R4,=F'3' z/3
ST R5,ZZ z=z/3
LA R4,0 z
D R4,=F'3' z/3
ENDDO , enddo while
LA R7,5 do j=5 by 2 while j<=z and j*j<=n
WHILEJ C R7,ZZ if j>z
BH EWHILEJ then leave while
LR R5,R7 j
MR R4,R7 *j
C R5,N if j*j>n
BH EWHILEJ then leave while
LR R4,R7 j
SRDA R4,32 ~
D R4,=F'3' j/3
LTR R4,R4 if j//3=0
BZ ITERJ then goto iterj
L R4,ZZ z
SRDA R4,32 ~
DR R4,R7 z/j
DO WHILE=(LTR,R4,Z,R4) do while z//j=0
LA R9,1(R9) f=f+1
LR R1,R7 j
BAL R14,SUMD call sumd(j)
AR R8,R0 m=m+sumd(j)
L R4,ZZ z
SRDA R4,32 ~
DR R4,R7 z/j
ST R5,ZZ z=z/j
LA R4,0 ~
DR R4,R7 z/j
ENDDO , enddo while
ITERJ LA R7,2(R7) j+=2
B WHILEJ enddo
EWHILEJ L R4,ZZ z
IF C,R4,NE,=F'1' THEN if z<>1 then
LA R9,1(R9) f=f+1
L R1,ZZ z
BAL R14,SUMD call sumd(z)
AR R8,R0 m=m+sumd(z)
ENDIF , endif
IF C,R9,LT,=F'2' THEN if f<2 then
SR R8,R8 mm=0
ENDIF , endif
LR R0,R8 return m
L R14,SAVER14 restore r14
BR R14 return
SAVER14 DS A save r14
- ---- ----------------------------------------
N DC F'10000' n NN DC F'0' nn IPG DC F'0' ipg SS DS F ss ZZ DS F z PG DC CL80' ' buffer PGT DC CL80'xxxx smith numbers found <= xxxxx' XDEC DS CL12 temp
YREGS
END SMITHNUM</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985 376 smith numbers found <= 10000
Ada
<lang ada> with Ada.Text_IO;
procedure smith is
type Vector is array (natural range <>) of Positive; empty_vector : constant Vector(1..0):= (others=>1); function digits_sum (n : Positive) return Positive is (if n < 10 then n else n mod 10 + digits_sum (n / 10));
function prime_factors (n : Positive; d : Positive := 2) return Vector is (if n = 1 then empty_vector elsif n mod d = 0 then prime_factors (n / d, d) & d else prime_factors (n, d + (if d=2 then 1 else 2))); function vector_digits_sum (v : Vector) return Natural is (if v'Length = 0 then 0 else digits_sum (v(v'First)) + vector_digits_sum (v(v'First+1..v'Last)));
begin
for n in 1..10000 loop
declare
primes : Vector := prime_factors (n);
begin
if primes'Length > 1 and then vector_digits_sum (primes) = digits_sum (n) then
Ada.Text_IO.put (n'img);
end if;
end;
end loop;
end smith; </lang>
ALGOL 68
<lang algol68># sieve of Eratosthene: sets s[i] to TRUE if i is prime, FALSE otherwise # PROC sieve = ( REF[]BOOL s )VOID:
BEGIN
# start with everything flagged as prime #
FOR i TO UPB s DO s[ i ] := TRUE OD;
# sieve out the non-primes #
s[ 1 ] := FALSE;
FOR i FROM 2 TO ENTIER sqrt( UPB s ) DO
IF s[ i ] THEN FOR p FROM i * i BY i TO UPB s DO s[ p ] := FALSE OD FI
OD
END # sieve # ;
- construct a sieve of primes up to the maximum number required for the task #
INT max number = 10 000; [ 1 : max number ]BOOL is prime; sieve( is prime );
- returns the sum of the digits of n #
OP DIGITSUM = ( INT n )INT:
BEGIN
INT sum := 0;
INT rest := ABS n;
WHILE rest > 0 DO
sum +:= rest MOD 10;
rest OVERAB 10
OD;
sum
END # DIGITSUM # ;
- returns TRUE if n is a Smith number, FALSE otherwise #
- n must be between 1 and max number #
PROC is smith = ( INT n )BOOL:
IF is prime[ ABS n ] THEN
# primes are not Smith numbers #
FALSE
ELSE
# find the factors of n and sum the digits of the factors #
INT rest := ABS n;
INT factor digit sum := 0;
INT factor := 2;
WHILE factor < max number AND rest > 1 DO
IF NOT is prime[ factor ] THEN
# factor isn't a prime #
factor +:= 1
ELSE
# factor is a prime #
IF rest MOD factor /= 0 THEN
# factor isn't a factor of n #
factor +:= 1
ELSE
# factor is a factor of n #
rest OVERAB factor;
factor digit sum +:= DIGITSUM factor
FI
FI
OD;
( factor digit sum = DIGITSUM n )
FI # is smith # ;
- print all the Smith numbers below the maximum required #
INT smith count := 0; FOR n TO max number - 1 DO
IF is smith( n ) THEN
# have a smith number #
print( ( whole( n, -7 ) ) );
smith count +:= 1;
IF smith count MOD 10 = 0 THEN
print( ( newline ) )
FI
FI
OD; print( ( newline, "THere are ", whole( smith count, -7 ), " Smith numbers below ", whole( max number, -7 ), newline ) ) </lang>
- Output:
4 22 27 58 85 94 121 166 202 265
274 319 346 355 378 382 391 438 454 483
...
9717 9735 9742 9760 9778 9840 9843 9849 9861 9880
9895 9924 9942 9968 9975 9985
THere are 376 Smith numbers below 10000
Arturo
<lang rebol>digitSum: function [v][
n: new v
result: new 0
while [n > 0][
'result + n % 10
'n / 10
]
return result
]
smith?: function [z][
return
(prime? z) ? -> false
-> (digitSum z) = sum map factors.prime z 'num [digitSum num]
] found: 0 loop 1..10000 'x [
if smith? x [
found: found + 1
prints (pad to :string x 6) ++ " "
if 0 = found % 10 -> print ""
]
] print ""</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
AWK
<lang AWK>
- syntax: GAWK -f SMITH_NUMBERS.AWK
- converted from C
BEGIN {
limit = 10000
printf("Smith Numbers < %d:\n",limit)
for (a=4; a<limit; a++) {
num_factors = num_prime_factors(a)
if (num_factors < 2) {
continue
}
prime_factors(a)
if (sum_digits(a) == sum_factors(num_factors)) {
printf("%4d ",a)
if (++cr % 16 == 0) {
printf("\n")
}
}
delete arr
}
printf("\n")
exit(0)
} function num_prime_factors(x, p,pf) {
p = 2
pf = 0
if (x == 1) {
return(1)
}
while (1) {
if (!(x % p)) {
pf++
x = int(x/p)
if (x == 1) {
return(pf)
}
}
else {
p++
}
}
} function prime_factors(x, p,pf) {
p = 2
pf = 0
if (x == 1) {
arr[pf] = 1
}
else {
while (1) {
if (!(x % p)) {
arr[pf++] = p
x = int(x/p)
if (x == 1) {
return
}
}
else {
p++
}
}
}
} function sum_digits(x, sum,y) {
while (x) {
y = x % 10
sum += y
x = int(x/10)
}
return(sum)
} function sum_factors(x, a,sum) {
sum = 0
for (a=0; a<x; a++) {
sum += sum_digits(arr[a])
}
return(sum)
} </lang>
- Output:
Smith Numbers < 10000: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
C
<lang c>
- include <stdlib.h>
- include <stdio.h>
- include <stdbool.h>
int numPrimeFactors(unsigned x) {
unsigned p = 2;
int pf = 0;
if (x == 1)
return 1;
else {
while (true) {
if (!(x % p)) {
pf++;
x /= p;
if (x == 1)
return pf;
}
else
++p;
}
}
}
void primeFactors(unsigned x, unsigned* arr) {
unsigned p = 2;
int pf = 0;
if (x == 1)
arr[pf] = 1;
else {
while (true) {
if (!(x % p)) {
arr[pf++] = p;
x /= p;
if (x == 1)
return;
}
else
p++;
}
}
}
unsigned sumDigits(unsigned x) {
unsigned sum = 0, y;
while (x) {
y = x % 10;
sum += y;
x /= 10;
}
return sum;
}
unsigned sumFactors(unsigned* arr, int size) {
unsigned sum = 0;
for (int a = 0; a < size; a++)
sum += sumDigits(arr[a]);
return sum;
}
void listAllSmithNumbers(unsigned x) {
unsigned *arr;
for (unsigned a = 4; a < x; a++) {
int numfactors = numPrimeFactors(a);
arr = (unsigned*)malloc(numfactors * sizeof(unsigned));
if (numfactors < 2)
continue;
primeFactors(a, arr);
if (sumDigits(a) == sumFactors(arr,numfactors))
printf("%4u ",a);
free(arr);
}
}
int main(int argc, char* argv[]) {
printf("All the Smith Numbers < 10000 are:\n");
listAllSmithNumbers(10000);
return 0;
} </lang>
- Output:
All the Smith Numbers < 10000 are: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
C#
<lang csharp>using System; using System.Collections.Generic;
namespace SmithNumbers {
class Program {
static int SumDigits(int n) {
int sum = 0;
while (n > 0) {
n = Math.DivRem(n, 10, out int rem);
sum += rem;
}
return sum;
}
static List<int> PrimeFactors(int n) {
List<int> result = new List<int>();
for (int i = 2; n % i == 0; n /= i) {
result.Add(i);
}
for (int i = 3; i * i < n; i += 2) {
while (n % i == 0) {
result.Add(i);
n /= i;
}
}
if (n != 1) {
result.Add(n);
}
return result;
}
static void Main(string[] args) {
const int SIZE = 8;
int count = 0;
for (int n = 1; n < 10_000; n++) {
var factors = PrimeFactors(n);
if (factors.Count > 1) {
int sum = SumDigits(n);
foreach (var f in factors) {
sum -= SumDigits(f);
}
if (sum == 0) {
Console.Write("{0,5}", n);
if (count == SIZE - 1) {
Console.WriteLine();
}
count = (count + 1) % SIZE;
}
}
}
}
}
}</lang>
- Output:
4 22 27 58 85 94 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2166 2173 2182 2218 2227 2265 2286 2326 2362 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5926 5935 5936 5946 5998 6036 6054 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7935 7938 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9387 9396 9414 9427 9483 9535 9537 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
C++
<lang cpp>
- include <iostream>
- include <vector>
- include <iomanip>
void primeFactors( unsigned n, std::vector<unsigned>& r ) {
int f = 2; if( n == 1 ) r.push_back( 1 );
else {
while( true ) {
if( !( n % f ) ) {
r.push_back( f );
n /= f; if( n == 1 ) return;
}
else f++;
}
}
} unsigned sumDigits( unsigned n ) {
unsigned sum = 0, m;
while( n ) {
m = n % 10; sum += m;
n -= m; n /= 10;
}
return sum;
} unsigned sumDigits( std::vector<unsigned>& v ) {
unsigned sum = 0;
for( std::vector<unsigned>::iterator i = v.begin(); i != v.end(); i++ ) {
sum += sumDigits( *i );
}
return sum;
} void listAllSmithNumbers( unsigned n ) {
std::vector<unsigned> pf;
for( unsigned i = 4; i < n; i++ ) {
primeFactors( i, pf ); if( pf.size() < 2 ) continue;
if( sumDigits( i ) == sumDigits( pf ) )
std::cout << std::setw( 4 ) << i << " ";
pf.clear();
}
std::cout << "\n\n";
} int main( int argc, char* argv[] ) {
listAllSmithNumbers( 10000 ); return 0;
} </lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 627 634 636 645 663 666 690 ... 9301 9330 9346 9355 9382 9386 9387 9396 9427 9483 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9843 9849 9861 9880 9895 9975 9985
Clojure
<lang clojure>(defn divisible? [a b]
(zero? (mod a b)))
(defn prime? [n]
(and (> n 1) (not-any? (partial divisible? n) (range 2 n))))
(defn prime-factors
([n] (prime-factors n 2 '()))
([n candidate acc]
(cond
(<= n 1) (reverse acc)
(zero? (rem n candidate)) (recur
(/ n candidate)
candidate
(cons candidate acc))
:else (recur n (inc candidate) acc))))
(defn sum-digits [n]
(reduce + (map #(- (int %) (int \0)) (str n))))
(defn smith-number? [n]
(and (not (prime? n))
(= (sum-digits n)
(sum-digits (clojure.string/join "" (prime-factors n))))))
(filter smith-number? (range 1 10000))</lang>
- Output:
(4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 ... 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985)
D
mostly
<lang D>import std.stdio;
void main() {
int cnt;
for (int n=1; n<10_000; n++) {
auto factors = primeFactors(n);
if (factors.length > 1) {
int sum = sumDigits(n);
foreach (f; factors) {
sum -= sumDigits(f);
}
if (sum==0) {
writef("%4s ", n);
cnt++;
}
if (cnt==10) {
cnt = 0;
writeln();
}
}
}
}
auto primeFactors(int n) {
import std.array : appender; auto result = appender!(int[]);
for (int i=2; n%i==0; n/=i) {
result.put(i);
}
for (int i=3; i*i<=n; i+=2) {
while (n%i==0) {
result.put(i);
n/=i;
}
}
if (n!=1) {
result.put(n);
}
return result.data;
}
int sumDigits(int n) {
int sum;
while (n > 0) {
sum += (n%10);
n /= 10;
}
return sum;
}</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Delphi
See Pascal.
Elixir
<lang elixir>defmodule Smith do
def number?(n) do d = decomposition(n) length(d)>1 and sum_digits(n) == Enum.map(d, &sum_digits/1) |> Enum.sum end defp sum_digits(n) do Integer.digits(n) |> Enum.sum end defp decomposition(n, k\\2, acc\\[]) defp decomposition(n, k, acc) when n < k*k, do: [n | acc] defp decomposition(n, k, acc) when rem(n, k) == 0, do: decomposition(div(n, k), k, [k | acc]) defp decomposition(n, k, acc), do: decomposition(n, k+1, acc)
end
m = 10000 smith = Enum.filter(1..m, &Smith.number?/1) IO.puts "#{length(smith)} smith numbers below #{m}:" IO.puts "First 10: #{Enum.take(smith,10) |> Enum.join(", ")}" IO.puts "Last 10: #{Enum.take(smith,-10) |> Enum.join(", ")}"</lang>
- Output:
376 smith numbers below 10000: First 10: 4, 22, 27, 58, 85, 94, 121, 166, 202, 265 Last 10: 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // Generate Smith Numbers. Nigel Galloway: November 6th., 2020 let fN g=Seq.unfold(fun n->match n with 0->None |_->Some(n%10,n/10)) g |> Seq.sum let rec fG(n,g) p=match g%p with 0->fG (n+fN p,g/p) p |_->(n,g) primes32()|>Seq.pairwise|>Seq.collect(fun(n,g)->[n+1..g-1])|>Seq.takeWhile(fun n->n<10000) |>Seq.filter(fun g->fN g=fst(primes32()|>Seq.scan(fun n g->fG n g)(0,g)|>Seq.find(fun(_,n)->n=1))) |>Seq.chunkBySize 20|>Seq.iter(fun n->Seq.iter(printf "%4d ") n; printfn "") </lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Factor
<lang>USING: formatting grouping io kernel math.primes.factors math.ranges math.text.utils sequences sequences.deep ;
- (smith?) ( n factors -- ? )
[ 1 digit-groups sum ] [ [ 1 digit-groups ] map flatten sum = ] bi* ; inline
- smith? ( n -- ? )
dup factors dup length 1 = [ 2drop f ] [ (smith?) ] if ;
10,000 [1,b] [ smith? ] filter 10 group [ [ "%4d " printf ] each nl ] each</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Fortran
This is F90 style, to take advantage of module PRIMESTUFF from Extensible_prime_generator to get at a supply of prime numbers and related routines, and contains a slightly trimmed module FACTORISE from the FRACTRAN project that factorises a number but which doesn't need the slight extras for the FRACTRAN process. Re-using code is good, but one must watch out for forgotten details that may not fit into the new context: the FRACTRAN project wanted the number of the prime, not the prime number (itself) in its lists of factors, whereas this project wanted the actual prime number in its list of factors. So, it would be PRIME(F.PNUM(i)), because "PNUM" means "the prime's number"... However, acquiring the i'th prime via PRIME(i) is not a matter of array access, it involves a function with some fancy arithmetic. Since the factorisation requires consecutive prime numbers, using NEXTPRIME(F) is a better choice, and the run is much faster since many numbers are being factorised: the FRACTRAN project factorised only a few. So, a change from "PNUM" to "PVAL" with the prime's value stored instead of its index, even though this means that PNUM(0) which holds the number of prime factors becomes PVAL(0): discordance in the mnemonics. Then, having started along these lines, a rewrite was provoked, prompted by the recollection that function ISPRIME does not engage in the standard slog through possible prime factors (except for two), since for odd numbers it refers to its big bit array. Accessing this array takes time as it is in a disc file, but the operating system buffers popular records in memory (a record is 4096 bytes for 32736 bits as each starts with a four-byte count, thus the first record spans 3 to 65473), so timing runs is a frustrating business. There seemed no gross change in speed, so that's good enough for a demonstration. The code involves a GO TO statement because there is no repeat ... until test construction provided in Fortran and a DO WHILE ... END DO would involve a wasted first test. Because I really hate array bound errors there is a check against LASTP even though the array will never overflow for INTEGER*4, but (potentially) someday the code might be inflated to INTEGER*8 or some other larger capacity and the necessary adjustments be overlooked. One could have IF (LASTP.LE.9 .AND. HUGE(N).GT.2147483648) STOP "Oi! INTEGER*4 usage!" to check this (and a good compiler would convert it to no code if all was well) but that's tiresome too and only checks for some problems. Accordingly, the code for adding a factor to the list is too messy to replicate, and making it into a service subroutine is tiresome: thus does structure falter when spaghetti is not forgotten.
Similarly, initial attempts foundered before I realised that the sum of the digits of the prime factors did not mean that of the unique prime factors once only but included each appearance of a prime factor, so it was DIGITSUM(F.PVAL(i),BASE)*F.PPOW(i) for success. And, since one is deemed to have no prime factors, one does not appear even though it is not skipped as being a prime number.
The factorisation is represented in a data aggregate, which is returned by function FACTOR. This is a facility introduced with F90, and before that one would have to use a collection of ordinary arrays to identify the list of primes and powers of a factorisation because functions could only return simple variables. Also, earlier compilers did not allow the use of the function's name as a variable within the function, or might allow this but produce incorrect results. However, modern facilities are not always entirely beneficial. Here, the function returns a full set of data for type FACTORED, even though often only the first few elements of the arrays will be needed and the rest could be ignored. It is possible to declare the arrays of type FACTORED to be "allocatable" with their size being determined at run time for each invocation of function FACTOR, at the cost of a lot of additional syntax and statements, plus the common annoyance of not knowing "how big" until after the list has been produced. Alas, such arrangements incur a performance penalty with every reference to the allocatable entities. See for example Sequence_of_primorial_primes#Run-time_allocation
For layout purposes, the numbers found were stashed in a line buffer rather than attempt to mess with the latter-day facilities of "non-advancing" output. This should be paramaterised for documentation purposes with say MBUF = 20 rather than just using the magic constant of 20, however getting that into the FORMAT statement would require FORMAT(<MBUF>I6) and this <n> facility may not be recognised. Alternatively, one could put FORMAT(666I6) and hope that MBUF would never exceed 666. <lang Fortran> MODULE FACTORISE !Produce a little list...
USE PRIMEBAG !This is a common need.
INTEGER LASTP !Some size allowances.
PARAMETER (LASTP = 9) !2*3*5*7*11*13*17*19*23*29 = 6,469,693,230, > 2,147,483,647.
TYPE FACTORED !Represent a number fully factored.
INTEGER PVAL(0:LASTP) !As a list of prime number indices with PVAL(0) the count.
INTEGER PPOW(LASTP) !And the powers. for the fingered primes.
END TYPE FACTORED !Rather than as a simple number multiplied out.
CONTAINS !Now for the details.
SUBROUTINE SHOWFACTORS(N) !First, to show an internal data structure.
TYPE(FACTORED) N !It is supplied as a list of prime factors.
INTEGER I !A stepper.
DO I = 1,N.PVAL(0) !Step along the list.
IF (I.GT.1) WRITE (MSG,"('x',$)") !Append a glyph for "multiply".
WRITE (MSG,"(I0,$)") N.PVAL(I) !The prime number's value.
IF (N.PPOW(I).GT.1) WRITE (MSG,"('^',I0,$)") N.PPOW(I) !With an interesting power?
END DO !On to the next element in the list.
WRITE (MSG,1) N.PVAL(0) !End the line
1 FORMAT (": Factor count ",I0) !With a count of prime factors.
END SUBROUTINE SHOWFACTORS !Hopefully, this will not be needed often.
TYPE(FACTORED) FUNCTION FACTOR(IT) !Into a list of primes and their powers.
Careful! 1 is not a factor of N, but if N is prime, N is. N = product of its prime factors.
INTEGER IT,N !The number and a similar style copy to damage.
INTEGER F,FP !A factor and a power.
IF (IT.LE.0) STOP "Factor only positive numbers!" !Or else...
FACTOR.PVAL(0) = 0 !No prime factors have been found. One need not apply.
F = 0 !NEXTPRIME(F) will return 2, the first factor to try.
N = IT !A copy I can damage.
Collapse N into its prime factors.
10 DO WHILE(N.GT.1) !Carthaga delenda est?
IF (ISPRIME(N)) THEN!If the remnant is a prime number,
F = N !Then it is the last factor.
FP = 1 !Its power is one.
N = 1 !And the reduction is finished.
ELSE !Otherwise, continue trying larger factors.
FP = 0 !It has no power yet.
11 F = NEXTPRIME(F) !Go for the next possible factor.
DO WHILE(MOD(N,F).EQ.0) !Well?
FP = FP + 1 !Count a factor..
N = N/F !Reduce the number.
END DO !Until F's multiplicity is exhausted.
IF (FP.LE.0) GO TO 11 !No presence? Try the next factor: N has some...
END IF !One way or another, F is a prime factor and FP its power.
IF (FACTOR.PVAL(0).GE.LASTP) THEN !Have I room in the list?
WRITE (MSG,1) IT,LASTP !Alas.
1 FORMAT ("Factoring ",I0," but with provision for only ", !This shouldn't happen,
1 I0," distinct prime factors!") !If LASTP is correct for the current INTEGER size.
CALL SHOWFACTORS(FACTOR) !Show what has been found so far.
STOP "Not enough storage!" !Quite.
END IF !But normally,
FACTOR.PVAL(0) = FACTOR.PVAL(0) + 1 !Admit another factor.
FACTOR.PVAL(FACTOR.PVAL(0)) = F !The prime number found to be a factor.
FACTOR.PPOW(FACTOR.PVAL(0)) = FP !Place its power.
END DO !Now seee what has survived.
END FUNCTION FACTOR !Thus, a list of primes and their powers.
END MODULE FACTORISE !Careful! PVAL(0) is the number of prime factors.
MODULE SMITHSTUFF !Now for the strange stuff.
CONTAINS !The two special workers.
INTEGER FUNCTION DIGITSUM(N,BASE) !Sums the digits of N.
INTEGER N,IT !The number, and a copy I can damage.
INTEGER BASE !The base for arithmetic,
IF (N.LT.0) STOP "DigitSum: negative numbers need not apply!"
DIGITSUM = 0 !Here we go.
IT = N !This value will be damaged.
DO WHILE(IT.GT.0) !Something remains?
DIGITSUM = MOD(IT,BASE) + DIGITSUM !Yes. Grap the low-order digit.
IT = IT/BASE !And descend a power.
END DO !Perhaps something still remains.
END FUNCTION DIGITSUM !Numerology.
LOGICAL FUNCTION SMITHNUM(N,BASE) !Worse numerology.
USE FACTORISE !To find the prime factord of N.
INTEGER N !The number of interest.
INTEGER BASE !The base of the numerology.
TYPE(FACTORED) F !A list.
INTEGER I,FD !Assistants.
F = FACTOR(N) !Hopefully, LASTP is large enough for N.
c write (6,"(a,I0,1x)",advance="no") "N=",N c call ShowFactors(F)
FD = 0 !Attempts via the SUM facility involved too many requirements.
DO I = 1,F.PVAL(0) !For each of the prime factors found...
FD = DIGITSUM(F.PVAL(I),BASE)*F.PPOW(I) + FD !Not forgetting the multiplicity.
END DO !On to the next prime factor in the list.
SMITHNUM = FD.EQ.DIGITSUM(N,BASE) !This is the rule.
END FUNCTION SMITHNUM !So, is N a joker?
END MODULE SMITHSTUFF !Simple enough.
USE PRIMEBAG !Gain access to GRASPPRIMEBAG.
USE SMITHSTUFF !The special stuff.
INTEGER LAST !Might as well document this.
PARAMETER (LAST = 9999) !The specification is BELOW 10000...
INTEGER I,N,BASE !Workers.
INTEGER NB,BAG(20) !Prepare a line's worth of results.
MSG = 6 !Standard output.
WRITE (MSG,1) LAST !Hello.
1 FORMAT ('To find the "Smith" numbers up to ',I0)
IF (.NOT.GRASPPRIMEBAG(66)) STOP "Gan't grab my file!" !Attempt in hope.
10 DO BASE = 2,12 !Flexible numerology.
WRITE (MSG,11) BASE !Here we go again.
11 FORMAT (/,"Working in base ",I0)
N = 0 !None found.
NB = 0 !So, none are bagged.
DO I = 1,LAST !Step through the span.
IF (ISPRIME(I)) CYCLE !Prime numbers are boring Smith numbers. Skip them.
IF (SMITHNUM(I,BASE)) THEN !So?
N = N + 1 !Count one in.
IF (NB.GE.20) THEN !A full line's worth with another to come?
WRITE (MSG,12) BAG !Yep. Roll the line to make space.
12 FORMAT (20I6) !This will do for a nice table.
NB = 0 !The line is now ready.
END IF !So much for a line buffer.
NB = NB + 1 !Count another entry.
BAG(NB) = I !Place it.
END IF !So much for a Smith style number.
END DO !On to the next candidate number.
WRITE (MSG,12) BAG(1:NB)!Wave the tail end.
WRITE (MSG,13) N !Save the human some counting.
13 FORMAT (I9," found.") !Just in case.
END DO !On to the next base.
END !That was strange.</lang>
Output: selecting the base ten result:
Working in base 10
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483
517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778
...etc
9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708
9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
376 found.
For the various bases, the counts were
Base: 2 3 4 5 6 7 8 9 10 11 12 Count: 615 459 417 327 716 245 432 250 376 742 448
Reverting to counting each prime of a factorisation once only did not simply reject all those Smith numbers that had repeated prime factors, it added new entries, for example 9940: the "smith" numbers?
Working in base 10
22 58 84 85 94 136 160 166 202 234 250 265 274 308 319 336 346 355 361 364
382 391 424 438 454 456 476 483 516 517 526 535 562 627 634 644 645 650 654 660
663 690 702 706 732 735 762 778 855 860 861 895 913 915 922 948 958 985 1086 1111
1116 1148 1165 1219 1255 1282 1312 1344 1404 1484 1507 1550 1576 1581 1600 1612 1626 1633 1642 1650
1665 1678 1708 1752 1795 1812 1822 1824 1842 1858 1876 1894 1903 1921 1924 1966 2008 2038 2064 2067
2106 2155 2166 2173 2182 2218 2227 2232 2236 2265 2275 2325 2326 2352 2356 2362 2373 2401 2409 2434
2461 2500 2515 2541 2565 2578 2605 2614 2616 2625 2640 2679 2722 2751 2760 2785 2826 2839 2872 2902
2911 2924 2958 2960 2965 2974 3036 3042 3046 3048 3091 3138 3164 3172 3226 3246 3268 3285 3339 3344
3345 3381 3390 3393 3442 3474 3476 3484 3505 3552 3556 3592 3595 3615 3618 3622 3625 3630 3649 3694
3712 3736 3792 3802 3836 3850 3865 3892 3912 3920 3930 3933 3946 3973 4024 4054 4116 4126 4148 4160
4162 4173 4188 4189 4191 4198 4209 4212 4228 4235 4268 4275 4279 4306 4344 4369 4396 4414 4456 4460
4473 4564 4590 4594 4636 4656 4676 4702 4744 4765 4770 4776 4794 4820 4824 4844 4855 4905 4918 4920
4954 4974 4980 4981 5022 5052 5062 5068 5071 5094 5098 5145 5150 5168 5176 5242 5253 5268 5269 5298
5305 5332 5344 5348 5386 5397 5412 5422 5425 5458 5464 5484 5485 5525 5539 5548 5602 5612 5638 5642
5652 5674 5715 5742 5752 5818 5840 5854 5874 5926 5935 5946 5998 6016 6027 6054 6060 6066 6115 6175
6178 6184 6187 6244 6259 6260 6295 6315 6356 6364 6385 6390 6439 6457 6472 6475 6500 6502 6504 6512
6524 6531 6564 6567 6583 6585 6596 6600 6603 6604 6616 6620 6633 6692 6693 6702 6714 6718 6741 6835
6855 6900 6904 6934 6950 6960 6980 6981 7008 7026 7028 7038 7048 7051 7052 7062 7076 7078 7089 7150
7186 7195 7196 7212 7228 7236 7249 7268 7287 7335 7339 7362 7364 7402 7428 7438 7447 7465 7503 7506
7525 7624 7627 7650 7674 7683 7726 7756 7762 7782 7809 7834 7850 7915 7924 7978 8005 8014 8023 8076
8077 8084 8091 8095 8145 8149 8158 8164 8185 8214 8224 8244 8257 8277 8284 8292 8308 8325 8334 8347
8415 8420 8421 8466 8508 8518 8545 8600 8653 8673 8720 8724 8754 8780 8790 8816 8851 8914 8924 8932
8955 8982 9015 9028 9031 9052 9094 9096 9116 9166 9180 9193 9229 9274 9285 9294 9301 9306 9330 9333
9346 9350 9355 9382 9412 9425 9427 9436 9483 9528 9535 9540 9571 9598 9630 9634 9650 9652 9711 9716
9717 9735 9742 9772 9778 9843 9861 9895 9916 9940 9942 9985
492 found.
FreeBASIC
<lang freebasic>' FB 1.05.0 Win64
Sub getPrimeFactors(factors() As UInteger, n As UInteger)
If n < 2 Then Return
Dim factor As UInteger = 2
Do
If n Mod factor = 0 Then
Redim Preserve factors(0 To UBound(factors) + 1)
factors(UBound(factors)) = factor
n \= factor
If n = 1 Then Return
Else
' non-prime factors will always give a remainder > 0 as their own factors have already been removed
' so it's not worth checking that the next potential factor is prime
factor += 1
End If
Loop
End Sub
Function sumDigits(n As UInteger) As UInteger
If n < 10 Then Return n Dim sum As UInteger = 0 While n > 0 sum += n Mod 10 n \= 10 Wend Return sum
End Function
Function isSmith(n As UInteger) As Boolean
If n < 2 Then Return False Dim factors() As UInteger getPrimeFactors factors(), n If UBound(factors) = 0 Then Return False n must be prime if there's only one factor Dim primeSum As UInteger = 0 For i As UInteger = 0 To UBound(factors) primeSum += sumDigits(factors(i)) Next Return sumDigits(n) = primeSum
End Function
Print "The Smith numbers below 10000 are : " Print Dim count As UInteger = 0 For i As UInteger = 2 To 9999
If isSmith(i) Then Print Using "#####"; i; count += 1 End If
Next Print : Print Print count; " numbers found" Print Print "Press any key to quit" Sleep</lang>
- Output:
The Smith numbers below 10000 are :
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382
391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654
663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958
985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678
1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962
1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409
2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751
2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168
3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663
3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191
4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788
4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242
5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642
5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115
6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583
6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062
7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503
7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978
8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347
8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851
8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285
9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571
9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849
9861 9880 9895 9924 9942 9968 9975 9985
376 numbers found
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
Go
<lang Go> package main
import "fmt"
func numPrimeFactors(x uint) int { var p uint = 2 var pf int if x == 1 { return 1 } for { if (x % p) == 0 { pf++ x /= p if x == 1 { return pf } } else { p++ } } }
func primeFactors(x uint, arr []uint) { var p uint = 2 var pf int if x == 1 { arr[pf] = 1 return } for { if (x % p) == 0 { arr[pf] = p pf++ x /= p if x == 1 { return } } else { p++ } } }
func sumDigits(x uint) uint { var sum uint for x != 0 { sum += x % 10 x /= 10 } return sum }
func sumFactors(arr []uint, size int) uint { var sum uint for a := 0; a < size; a++ { sum += sumDigits(arr[a]) } return sum }
func listAllSmithNumbers(maxSmith uint) { var arr []uint var a uint for a = 4; a < maxSmith; a++ { numfactors := numPrimeFactors(a) arr = make([]uint, numfactors) if numfactors < 2 { continue } primeFactors(a, arr) if sumDigits(a) == sumFactors(arr, numfactors) { fmt.Printf("%4d ", a) } } }
func main() { const maxSmith = 10000 fmt.Printf("All the Smith Numbers less than %d are:\n", maxSmith) listAllSmithNumbers(maxSmith) fmt.Println() } </lang>
- Output:
All the Smith Numbers less than 10000 are:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 56425674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Haskell
<lang haskell>import Data.Numbers.Primes (primeFactors) import Data.List (unfoldr) import Data.Tuple (swap) import Data.Bool (bool)
isSmith :: Int -> Bool isSmith n = pfs /= [n] && sumDigits n == foldr ((+) . sumDigits) 0 pfs
where sumDigits = sum . baseDigits 10 pfs = primeFactors n
baseDigits :: Int -> Int -> [Int] baseDigits base = unfoldr remQuot
where remQuot 0 = Nothing remQuot x = Just (swap (quotRem x base))
lowSmiths :: [Int] lowSmiths = filter isSmith [2 .. 9999]
lowSmithCount :: Int lowSmithCount = length lowSmiths
main :: IO () main =
mapM_ putStrLn [ "Count of Smith Numbers below 10k:" , show lowSmithCount , "\nFirst 15 Smith Numbers:" , unwords (show <$> take 15 lowSmiths) , "\nLast 12 Smith Numbers below 10k:" , unwords (show <$> drop (lowSmithCount - 12) lowSmiths) ]</lang>
- Output:
Count of Smith Numbers below 10k: 376 First 15 Smith Numbers: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 Last 12 Smith Numbers below 10k: 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
J
Implementation: <lang J>digits=: 10&#.inv sumdig=: +/@,@digits notprime=: -.@(1&p:) smith=: #~ notprime * (=&sumdig q:)every</lang>
Task example: <lang J> #smith }.i.10000 376
q:376
2 2 2 47
47 8$smith }.i.10000 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284
1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985</lang>
(first we count how many smith numbers are in our result, then we look at the prime factors of that count - turns out that 8 columns of 47 numbers each is perfect for this task.)
Java
<lang java>import java.util.*;
public class SmithNumbers {
public static void main(String[] args) {
for (int n = 1; n < 10_000; n++) {
List<Integer> factors = primeFactors(n);
if (factors.size() > 1) {
int sum = sumDigits(n);
for (int f : factors)
sum -= sumDigits(f);
if (sum == 0)
System.out.println(n);
}
}
}
static List<Integer> primeFactors(int n) {
List<Integer> result = new ArrayList<>();
for (int i = 2; n % i == 0; n /= i)
result.add(i);
for (int i = 3; i * i <= n; i += 2) {
while (n % i == 0) {
result.add(i);
n /= i;
}
}
if (n != 1)
result.add(n);
return result; }
static int sumDigits(int n) {
int sum = 0;
while (n > 0) {
sum += (n % 10);
n /= 10;
}
return sum;
}
}</lang>
4 22 27 58 85 94 121 ... 9924 9942 9968 9975 9985
JavaScript
ES6
<lang JavaScript>(() => {
'use strict';
// isSmith :: Int -> Bool
const isSmith = n => {
const pfs = primeFactors(n);
return (1 < pfs.length || n !== pfs[0]) && (
sumDigits(n) === pfs.reduce(
(a, x) => a + sumDigits(x),
0
)
);
};
// TEST -----------------------------------------------
// main :: IO ()
const main = () => {
// lowSmiths :: [Int]
const lowSmiths = enumFromTo(2)(9999)
.filter(isSmith);
// lowSmithCount :: Int
const lowSmithCount = lowSmiths.length;
return [
"Count of Smith Numbers below 10k:",
show(lowSmithCount),
"\nFirst 15 Smith Numbers:",
unwords(take(15)(lowSmiths)),
"\nLast 12 Smith Numbers below 10000:",
unwords(drop(lowSmithCount - 12)(lowSmiths))
].join('\n');
};
// SMITH ----------------------------------------------
// primeFactors :: Int -> [Int]
const primeFactors = x => {
const go = n => {
const fs = take(1)(
dropWhile(x => 0 != n % x)(
enumFromTo(2)(
floor(sqrt(n))
)
)
);
return 0 === fs.length ? [n] : fs.concat(
go(floor(n / fs[0]))
);
};
return go(x);
};
// sumDigits :: Int -> Int
const sumDigits = n =>
unfoldl(
x => 0 === x ? (
Nothing()
) : Just(quotRem(x)(10))
)(n).reduce((a, x) => a + x, 0);
// GENERIC --------------------------------------------
// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});
// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});
// Tuple (,) :: a -> b -> (a, b)
const Tuple = a => b => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// drop :: Int -> [a] -> [a]
// drop :: Int -> String -> String
const drop = n => xs =>
xs.slice(n)
// dropWhile :: (a -> Bool) -> [a] -> [a]
// dropWhile :: (Char -> Bool) -> String -> String
const dropWhile = p => xs => {
const lng = xs.length;
return 0 < lng ? xs.slice(
until(i => i === lng || !p(xs[i]))(
i => 1 + i
)(0)
) : [];
};
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m => n =>
Array.from({
length: 1 + n - m
}, (_, i) => m + i);
// floor :: Num -> Int const floor = Math.floor;
// quotRem :: Int -> Int -> (Int, Int)
const quotRem = m => n =>
Tuple(Math.floor(m / n))(
m % n
);
// show :: a -> String const show = x => JSON.stringify(x, null, 2);
// sqrt :: Num -> Num
const sqrt = n =>
(0 <= n) ? Math.sqrt(n) : undefined;
// sum :: [Num] -> Num const sum = xs => xs.reduce((a, x) => a + x, 0);
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = n => xs =>
'GeneratorFunction' !== xs.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
// unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
const unfoldl = f => v => {
let
xr = [v, v],
xs = [];
while (true) {
const mb = f(xr[0]);
if (mb.Nothing) {
return xs
} else {
xr = mb.Just;
xs = [xr[1]].concat(xs);
}
}
};
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = p => f => x => {
let v = x;
while (!p(v)) v = f(v);
return v;
};
// unwords :: [String] -> String
const unwords = xs => xs.join(' ');
return main();
})();</lang>
- Output:
Count of Smith Numbers below 10k: 376 First 15 Smith Numbers: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 Last 12 Smith Numbers below 10000: 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Julia
<lang julia># v0.6
function sumdigits(n::Integer)
sum = 0
while n > 0
sum += n % 10
n = div(n, 10)
end
return sum
end
using Primes issmith(n::Integer) = !isprime(n) && sumdigits(n) == sum(sumdigits(f) for f in factor(Vector, n))
smithnumbers = collect(n for n in 2:10000 if issmith(n)) println("Smith numbers up to 10000:\n$smithnumbers")</lang>
- Output:
Smith numbers up to 10000: [4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]
Kotlin
<lang scala>// version 1.0.6
fun getPrimeFactors(n: Int): MutableList<Int> {
val factors = mutableListOf<Int>()
if (n < 2) return factors
var factor = 2
var nn = n
while (true) {
if (nn % factor == 0) {
factors.add(factor)
nn /= factor
if (nn == 1) return factors
}
else if (factor >= 3) factor += 2
else factor = 3
}
}
fun sumDigits(n: Int): Int = when {
n < 10 -> n
else -> {
var sum = 0
var nn = n
while (nn > 0) {
sum += (nn % 10)
nn /= 10
}
sum
}
}
fun isSmith(n: Int): Boolean {
if (n < 2) return false
val factors = getPrimeFactors(n)
if (factors.size == 1) return false
val primeSum = factors.sumBy { sumDigits(it) }
return sumDigits(n) == primeSum
}
fun main(args: Array<String>) {
println("The Smith numbers below 10000 are:\n")
var count = 0
for (i in 2 until 10000) {
if (isSmith(i)) {
print("%5d".format(i))
count++
}
}
println("\n\n$count numbers found")
}</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985 376 numbers found
Lua
Slightly long-winded prime factor function but it's a bit faster than the 'easy' way. <lang Lua>-- Returns a boolean indicating whether n is prime function isPrime (n)
if n < 2 then return false end
if n < 4 then return true end
if n % 2 == 0 then return false end
for d = 3, math.sqrt(n), 2 do
if n % d == 0 then return false end
end
return true
end
-- Returns a table of the prime factors of n function primeFactors (n)
local pfacs, divisor = {}, 1
if n < 1 then return pfacs end
while not isPrime(n) do
while not isPrime(divisor) do divisor = divisor + 1 end
while n % divisor == 0 do
n = n / divisor
table.insert(pfacs, divisor)
end
divisor = divisor + 1
if n == 1 then return pfacs end
end
table.insert(pfacs, n)
return pfacs
end
-- Returns the sum of the digits of n function sumDigits (n)
local sum, nStr = 0, tostring(n)
for digit = 1, nStr:len() do
sum = sum + tonumber(nStr:sub(digit, digit))
end
return sum
end
-- Returns a boolean indicating whether n is a Smith number function isSmith (n)
if isPrime(n) then return false end
local sumFacs = 0
for _, v in ipairs(primeFactors(n)) do
sumFacs = sumFacs + sumDigits(v)
end
return sumFacs == sumDigits(n)
end
-- Main procedure for n = 1, 10000 do
if isSmith(n) then io.write(n .. "\t") end
end</lang> Seems silly to paste in all 376 numbers but rest assured the output agrees with https://oeis.org/A006753
M2000 Interpreter
We make a 80X40 console, and prints 376 smith numbers, using 5 character column width, $(,5) leave first argument and pass second as column width. Using $(4,5) we can print proportional in columns (by default is 0, prints any font as monospaced font). In console we can mix any kind of text, bold, italics, colored and graphics too. Console is bitmap type, Text prints with transparent background, so to print over text, we have to clear first. This happen automatic with scrolling for last line (can be scroll reverse too). There are some variants for print statement and here we use Print Over to clear the line before, and we can make some temporary changes too.
We handle refresh from module (set fast! is for maximum speed), using refresh statement. We use Euler's Sieve, it is 10 times faster than Eratosthenes Sieve.
variable i used for For { } and change inside block, but structure For use own counter,so we get the right i (the next value), when block start again.
Not all factors calculated for a number, if sum of digits are greater than sum of digits of that number.
At the end we get a list (an inventory object with keys only). Print statement prints all keys (normally data, but if key isn't paired with data,then key is read only data)
<lang M2000 Interpreter> Module Checkit {
Set Fast !
Form 80, 40
Refresh
Function Smith(max=10000) {
Function SumDigit(a$) {
def long sum
For i=1 to len(a$) {sum+=val(mid$(a$,i, 1)) }
=sum
}
x=max
\\ Euler's Sieve
Dim r(x+1)=1
k=2
k2=k**2
While k2<x {
For m=k2 to x step k {r(m)=0}
Repeat {
k++ : k2=k**2
} Until r(k)=1 or k2>x
}
r(0)=0
smith=0
smith2=0
lastI=0
inventory smithnumbers
Top=max div 100
c=4
For i=4 to max {
if c> top then print over $(0,6), ceil(i/max*100);"%" : Refresh : c=1
c++
if r(i)=0 then {
smith=sumdigit(str$(i)) : lastI=i
smith2=0
do {
ii=int(sqrt(i))+1
do { ii-- : while r(ii)<>1 {ii--} } until i mod ii=0
if ii<2 then smith2+=sumdigit(str$(i)):exit
smith3=sumdigit(str$(ii))
do {
smith2+=smith3
i=i div ii : if ii<2 or i<2 then exit
} until i mod ii<>0 or smith2>smith
} until i<2 or smith2>smith
If smith=smith2 then Append smithnumbers, lastI
}
}
=smithnumbers
}
const MaxNumbers=10000
numbers= Smith(MaxNumbers)
Print
Print $(,5), numbers
Print
Print format$(" {0} smith numbers found <= {1}", Len(numbers), MaxNumbers)
} Checkit </lang>
MAD
<lang MAD> NORMAL MODE IS INTEGER
PRINT COMMENT$ SMITH NUMBERS$
R GENERATE PRIMES UP TO 10,000 USING SIEVE METHOD
BOOLEAN SIEVE
DIMENSION SIEVE(10000)
DIMENSION PRIMES(1500)
THROUGH SET, FOR I=2, 1, I.G.10000
SET SIEVE(I) = 1B
THROUGH NXPRIM, FOR P=2, 1, P.G.100
WHENEVER SIEVE(P)
THROUGH MARK, FOR I=P*P, P, I.G.10000
MARK SIEVE(I) = 0B NXPRIM END OF CONDITIONAL
NPRIMS = 0
THROUGH CNTPRM, FOR P=2, 1, P.G.10000
WHENEVER SIEVE(P)
PRIMES(NPRIMS) = P
NPRIMS = NPRIMS + 1
CNTPRM END OF CONDITIONAL
R CHECK SMITH NUMBERS
THROUGH SMITH, FOR I=4, 1, I.GE.10000
WHENEVER .NOT. SIEVE(I)
K = I
PFSUM = 0
THROUGH FACSUM, FOR P=0, 1, P.GE.NPRIMS .OR. K.E.0
L = PRIMES(P)
FACDIV WHENEVER K/L*L.E.K .AND. K.NE.0
PFSUM = PFSUM + DGTSUM.(L)
K = K/L
TRANSFER TO FACDIV
FACSUM END OF CONDITIONAL
WHENEVER PFSUM.E.DGTSUM.(I), PRINT FORMAT NUMFMT,I
SMITH END OF CONDITIONAL
VECTOR VALUES NUMFMT = $I5*$
R GET SUM OF DIGITS OF N
INTERNAL FUNCTION(N)
ENTRY TO DGTSUM.
DSUM = 0
DNUM = N
LOOP WHENEVER DNUM.E.0, FUNCTION RETURN DSUM
DSUM = DSUM + DNUM-DNUM/10*10
DNUM = DNUM/10
TRANSFER TO LOOP
END OF FUNCTION
END OF PROGRAM</lang>
- Output:
SMITH NUMBERS
4
22
27
58
85
94
121
166
202
265
274
319
346
355
378
382
391
438
454
483
517
526
535
562
576
588
627
634
636
645
648
654
663
666
690
706
728
729
762
778
825
852
861
895
913
915
922
958
985
1086
1111
1165
1219
1255
1282
1284
1376
1449
1507
1581
1626
1633
1642
1678
1736
1755
1776
1795
1822
1842
1858
1872
1881
1894
1903
1908
1921
1935
1952
1962
1966
2038
2067
2079
2155
2173
2182
2218
2227
2265
2286
2326
2362
2366
2373
2409
2434
2461
2475
2484
2515
2556
2576
2578
2583
2605
2614
2679
2688
2722
2745
2751
2785
2839
2888
2902
2911
2934
2944
2958
2964
2965
2970
2974
3046
3091
3138
3168
3174
3226
3246
3258
3294
3345
3366
3390
3442
3505
3564
3595
3615
3622
3649
3663
3690
3694
3802
3852
3864
3865
3930
3946
3973
4054
4126
4162
4173
4185
4189
4191
4198
4209
4279
4306
4369
4414
4428
4464
4472
4557
4592
4594
4702
4743
4765
4788
4794
4832
4855
4880
4918
4954
4959
4960
4974
4981
5062
5071
5088
5098
5172
5242
5248
5253
5269
5298
5305
5386
5388
5397
5422
5458
5485
5526
5539
5602
5638
5642
5674
5772
5818
5854
5874
5915
5926
5935
5936
5946
5998
6036
6054
6084
6096
6115
6171
6178
6187
6188
6252
6259
6295
6315
6344
6385
6439
6457
6502
6531
6567
6583
6585
6603
6684
6693
6702
6718
6760
6816
6835
6855
6880
6934
6981
7026
7051
7062
7068
7078
7089
7119
7136
7186
7195
7227
7249
7287
7339
7402
7438
7447
7465
7503
7627
7674
7683
7695
7712
7726
7762
7764
7782
7784
7809
7824
7834
7915
7952
7978
8005
8014
8023
8073
8077
8095
8149
8154
8158
8185
8196
8253
8257
8277
8307
8347
8372
8412
8421
8466
8518
8545
8568
8628
8653
8680
8736
8754
8766
8790
8792
8851
8864
8874
8883
8901
8914
9015
9031
9036
9094
9166
9184
9193
9229
9274
9276
9285
9294
9296
9301
9330
9346
9355
9382
9386
9387
9396
9414
9427
9483
9522
9535
9571
9598
9633
9634
9639
9648
9657
9684
9708
9717
9735
9742
9760
9778
9840
9843
9849
9861
9880
9895
9924
9942
9968
9975
9985
Maple
<lang Maple>isSmith := proc(n::posint) local factors, sumofDigits, sumofFactorDigits, x; if isprime(n) then
return false;
else
sumofDigits := add(x, x = convert(n, base, 10)); sumofFactorDigits := add(map(x -> op(convert(x, base, 10)), [op(NumberTheory:-PrimeFactors(n))])); return evalb(sumofDigits = sumofFactorDigits);
end if; end proc:
findSmith := proc(n::posint) return select(isSmith, [seq(1 .. n - 1)]); end proc:
findSmith(10000);</lang>
- Output:
[4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]
Mathematica/Wolfram Language
<lang Mathematica>smithQ[n_] := Not[PrimeQ[n]] &&
Total[IntegerDigits[n]] == Total[IntegerDigits /@ Flatten[ConstantArray @@@ FactorInteger[n]],2];
Select[Range[2, 10000], smithQ]</lang>
- Output:
{4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985}
Modula-2
<lang modula2>MODULE SmithNumbers; FROM FormatString IMPORT FormatString; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE SumDigits(n : INTEGER) : INTEGER; VAR sum : INTEGER; BEGIN
sum := 0;
WHILE n > 0 DO
sum := sum + (n MOD 10);
n := n DIV 10;
END;
RETURN sum;
END SumDigits;
VAR
n,i,j,fc,sum,rc : INTEGER; buf : ARRAY[0..63] OF CHAR;
BEGIN
rc := 0;
FOR i:=1 TO 10000 DO
n := i;
fc := 0;
sum := SumDigits(n);
j := 2;
WHILE n MOD j = 0 DO
INC(fc);
sum := sum - SumDigits(j);
n := n DIV j;
END;
j := 3;
WHILE j*j<=n DO
WHILE n MOD j = 0 DO
INC(fc);
sum := sum - SumDigits(j);
n := n DIV j;
END;
INC(j,2);
END;
IF n#1 THEN
INC(fc);
sum := sum - SumDigits(n);
END;
IF (fc>1) AND (sum=0) THEN
FormatString("%4i ", buf, i);
WriteString(buf);
INC(rc);
IF rc=10 THEN
rc := 0;
WriteLn;
END;
END;
END;
ReadChar;
END SmithNumbers.</lang>
Nim
<lang nim>import strformat
func primeFactors(n: int): seq[int] =
result = newSeq[int]()
var n = n
var i = 2
while n mod i == 0:
result.add(i)
n = n div i
i = 3
while i * i <= n:
while n mod i == 0:
result.add(i)
n = n div i
inc i, 2
if n != 1:
result.add(n)
func sumDigits(n: int): int =
var n = n var sum = 0 while n > 0: inc sum, n mod 10 n = n div 10 sum
var cnt = 0 for n in 1..10_000:
var factors = primeFactors(n)
if factors.len > 1:
var sum = sumDigits(n)
for f in factors:
dec sum, sumDigits(f)
if sum == 0:
stdout.write(&"{n:4} ")
inc cnt
if cnt == 10:
cnt = 0
stdout.write("\n")
echo()</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Objeck
<lang objeck>use Collection;
class Test {
function : Main(args : String[]) ~ Nil {
for(n := 1; n < 10000; n+=1;) {
factors := PrimeFactors(n);
if(factors->Size() > 1) {
sum := SumDigits(n);
each(i : factors) {
sum -= SumDigits(factors->Get(i));
};
if(sum = 0) {
n->PrintLine();
};
};
};
}
function : PrimeFactors(n : Int) ~ IntVector {
result := IntVector->New();
for(i := 2; n % i = 0; n /= i;) {
result->AddBack(i);
};
for(i := 3; i * i <= n; i += 2;) {
while(n % i = 0) {
result->AddBack(i);
n /= i;
};
};
if(n <> 1) {
result->AddBack(n);
};
return result;
}
function : SumDigits(n : Int) ~ Int {
sum := 0;
while(n > 0) {
sum += (n % 10);
n /= 10;
};
return sum;
}
}</lang>
4 22 27 58 85 94 121 166 202 ... 9975 9985
PARI/GP
<lang parigp>isSmith(n)=my(f=factor(n)); if(#f~==1 && f[1,2]==1, return(0)); sum(i=1, #f~, sumdigits(f[i, 1])*f[i, 2]) == sumdigits(n); select(isSmith, [1..9999])</lang>
- Output:
%1 = [4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]
2.6.0 introduced the forcomposite iterator, removing the need to check each term for primality.
<lang parigp>forcomposite(n=4,9999, f=factor(n); if(#f~==1 && f[1,2]==1, next); if(sum(i=1, #f~, sumdigits(f[i, 1])*f[i, 2]) == sumdigits(n), print1(n" ")))</lang>
2.10.0 gave us forfactored which speeds the process up by sieving for factors.
<lang parigp>forfactored(n=4,9999, f=n[2]; if(#f~==1 && f[1,2]==1, next); if(sum(i=1, #f~, sumdigits(f[i, 1])*f[i, 2]) == sumdigits(n[1]), print1(n[1]" ")))</lang>
Pascal
Using a segmented sieve of erathostenes and mark every number with the index of its prime factor <= sqrt(number). I use a presieved segment to reduce the time for small primes. I thought, it would be a small speed improvement ;-)
the function IncDgtSum delivers the next sum of digits very fast (2.6 s for 1 to 1e9 ) <lang pascal>program SmithNum; {$IFDEF FPC}
{$MODE objFPC} //result and useful for x64
{$CODEALIGN PROC=64}
{$ENDIF} uses
sysutils;
type
tdigit = byte; tSum = LongInt;
const
base = 10; //maxDigitCnt *(base-1) <= High(tSum) //maxDigitCnt <= High(tSum) DIV (base-1); maxDigitCnt = 16;
StartPrimNo = 6; csegsieveSIze = 2*3*5*7*11*13;//prime 0..5
type
tDgtSum = record
dgtNum : LongInt;
dgtSum : tSum;
dgts : array[0..maxDigitCnt-1] of tdigit;
end;
tNumFactype = word;
tnumFactor = record
numfacCnt: tNumFactype;
numfacts : array[1..15] of tNumFactype;
end;
tpnumFactor= ^tnumFactor;
tsieveprim = record
spPrim : Word;
spDgtsum : Word;
spOffset : LongWord;
end;
tpsieveprim = ^tsieveprim;
tsievePrimarr = array[0..6542-1] of tsieveprim; tsegmSieve = array[1..csegsieveSIze] of tnumFactor;
var
Primarr:tsievePrimarr; copySieve, actSieve : tsegmSieve; PrimDgtSum :tDgtSum; PrimCnt : NativeInt;
function IncDgtSum(var ds:tDgtSum):boolean; //add 1 to dgts and corrects sum of Digits //return if overflow happens var
i : NativeInt;
Begin
i := High(ds.dgts);
inc(ds.dgtNum);
repeat
IF ds.dgts[i] < Base-1 then
//add one and done
Begin
inc(ds.dgts[i]);
inc(ds.dgtSum);
BREAK;
end
else
Begin
ds.dgts[i] := 0;
dec(ds.dgtSum,Base-1);
end;
dec(i);
until i < Low(ds.dgts);
result := i < Low(ds.dgts)
end;
procedure OutDgtSum(const ds:tDgtSum); var
i : NativeInt;
Begin
i := Low(ds.dgts);
repeat
write(ds.dgts[i]:3);
inc(i);
until i > High(ds.dgts);
writeln(' sum of digits : ',ds.dgtSum:3);
end;
procedure OutSieve(var s:tsegmSieve); var
i,j : NativeInt;
Begin
For i := Low(s) to High(s) do
with s[i] do
Begin
write(i:6,numfacCnt:4);
For j := 1 to numfacCnt do
write(numFacts[j]:5);
writeln;
end;
end;
procedure SieveForPrimes; // sieve for all primes < High(Word) var
sieve : array of byte; pS : pByte; p,i : NativeInt;
Begin
setlength(sieve,High(Word));
Fillchar(sieve[Low(sieve)],length(sieve),#0);
pS:= @sieve[0]; //zero based
dec(pS);// make it one based
//sieve
p := 2;
repeat
i := p*p;
IF i> High(Word) then
BREAK;
repeat pS[i] := 1; inc(i,p); until i > High(Word);
repeat inc(p) until pS[p] = 0;
until false;
//now fill array of primes
fillchar(PrimDgtSum,SizeOf(PrimDgtSum),#0);
IncDgtSum(PrimDgtSum);//1
i := 0;
For p := 2 to High(Word) do
Begin
IncDgtSum(PrimDgtSum);
if pS[p] = 0 then
Begin
with PrimArr[i] do
Begin
spOffset := 2*p;//start at 2*prime
spPrim := p;
spDgtsum := PrimDgtSum.dgtSum;
end;
inc(i);
end;
end;
PrimCnt := i-1;
end;
procedure MarkWithPrime(SpIdx:NativeInt;var sf:tsegmSieve); var
i : NativeInt; pSf :^tnumFactor; MarkPrime : NativeInt;
Begin
with Primarr[SpIdx] do
Begin
MarkPrime := spPrim;
i := spOffSet;
IF i <= csegsieveSize then
Begin
pSf := @sf[i];
repeat
pSf^.numFacts[pSf^.numfacCnt+1] := SpIdx;
inc(pSf^.numfacCnt);
inc(pSf,MarkPrime);
inc(i,MarkPrime);
until i > csegsieveSize;
end;
spOffset := i-csegsieveSize;
end;
end;
procedure InitcopySieve(var cs:tsegmSieve); var
pr: NativeInt;
Begin
fillchar(cs[Low(cs)],sizeOf(cs),#0);
For Pr := 0 to 5 do
Begin
with Primarr[pr] do
spOffset := spPrim;//mark the prime too
MarkWithPrime(pr,cs);
end;
end;
procedure MarkNextSieve(var s:tsegmSieve); var
idx: NativeInt;
Begin
s:= copySieve; For idx := StartPrimNo to PrimCnt do MarkWithPrime(idx,s);
end;
function DgtSumInt(n: NativeUInt):NativeUInt; var
r : NativeUInt;
Begin
result := 0; repeat r := n div base; inc(result,n-base*r); n := r until r = 0;
end;
{function DgtSumOfFac(pN: tpnumFactor;dgtNo:tDgtSum):boolean;} function TestSmithNum(pN: tpnumFactor;dgtNo:tDgtSum):boolean; var
i,k,r,dgtSumI,dgtSumTarget : NativeUInt; pSp:tpsieveprim; pNumFact : ^tNumFactype;
Begin
i := dgtNo.dgtNum; dgtSumTarget :=dgtNo.dgtSum;
dgtSumI := 0; with pN^ do Begin k := numfacCnt; pNumFact := @numfacts[k]; end;
For k := k-1 downto 0 do
Begin
pSp := @PrimArr[pNumFact^];
r := i DIV pSp^.spPrim;
repeat
i := r;
r := r DIV pSp^.spPrim;
inc(dgtSumI,pSp^.spDgtsum);
until (i - r* pSp^.spPrim) <> 0;
IF dgtSumI > dgtSumTarget then
Begin
result := false;
EXIT;
end;
dec(pNumFact);
end;
If i <> 1 then
inc(dgtSumI,DgtSumInt(i));
result := dgtSumI = dgtSumTarget
end;
function CheckSmithNo(var s:tsegmSieve;var dgtNo:tDgtSum;Lmt:NativeInt=csegsieveSIze):NativeUInt; var
pNumFac : tpNumFactor; i : NativeInt;
Begin
result := 0;
i := low(s);
pNumFac := @s[i];
For i := i to lmt do
Begin
incDgtSum(dgtNo);
IF pNumFac^.numfacCnt<> 0 then
IF TestSmithNum(pNumFac,dgtNo) then
Begin
inc(result);
//Mark as smith number
inc(pNumFac^.numfacCnt,1 shl 15);
end;
inc(pNumFac);
end;
end;
const
limit = 100*1000*1000;
var
actualNo :tDgtSum; i,s : NativeInt;
Begin
SieveForPrimes; InitcopySieve(copySieve); i := 1; s:= -6;//- 2,3,5,7,11,13
fillchar(actualNo,SizeOf(actualNo),#0); while i < Limit-csegsieveSize do Begin MarkNextSieve(actSieve); inc(s,CheckSmithNo(actSieve,actualNo)); inc(i, csegsieveSize); end; //check the rest MarkNextSieve(actSieve); inc(s,CheckSmithNo(actSieve,actualNo,Limit-i+1)); write(s:8,' smith-numbers up to ',actualNo.dgtnum:10);
end.
</lang>
- Output:
64-Bit FPC 3.1.1 -O3 -Xs i4330 3.5 Ghz
6 smith-numbers up to 100
49 smith-numbers up to 1000
376 smith-numbers up to 10000
3294 smith-numbers up to 100000
29928 smith-numbers up to 1000000 real 0m00.064s
278411 smith-numbers up to 10000000 real 0m00.661s
2632758 smith-numbers up to 100000000 real 0m06.981s
25154060 smith-numbers up to 1000000000 real 1m14.077s
Number of Smith numbers below 10^n. 1
1:1, 2:6, 3:49, 4:376, 5:3294, 6:29928, 7:278411, 8:2632758,
9:25154060, 10:241882509, 11:2335807857, 12:22635291815,13:219935518608
Perl
<lang perl>use ntheory qw/:all/; my @smith; forcomposites {
push @smith, $_ if sumdigits($_) == sumdigits(join("",factor($_)));
} 10000-1; say scalar(@smith), " Smith numbers below 10000."; say "@smith";</lang>
- Output:
376 Smith numbers below 10000. 4 22 27 58 85 94 121 166 202 ... 9924 9942 9968 9975 9985
Version 0.71 of the ntheory module added forfactored, similar to Pari/GP's 2.10.0 addition. For large inputs this can halve the time taken compared to forcomposites.
<lang perl>use ntheory ":all";
my $t=0;
forfactored { $t++ if @_ > 1 && sumdigits($_) == sumdigits(join "",@_); } 10**8;
say $t;</lang>
Phix
<lang Phix>requires("0.8.2") -- (filter/apply were not available in 0.8.1 and earlier)
function sum_digits(integer n, integer base=10)
integer res = 0
while n do
res += remainder(n,base)
n = floor(n/base)
end while
return res
end function
function smith(integer n)
sequence p = prime_factors(n,true)
if length(p)=1 then return false end if
integer sp = sum(apply(p,sum_digits)),
sn = sum_digits(n)
return sn=sp
end function
sequence s = filter(tagset(10000),smith) ?shorten(s,"numbers",8)</lang>
- Output:
{4,22,27,58,85,94,121,166,"...",9861,9880,9895,9924,9942,9968,9975,9985," (376 numbers)"}
PicoLisp
<lang PicoLisp>(de factor (N)
(make
(let (D 2 L (1 2 2 . (4 2 4 2 4 6 2 6 .)) M (sqrt N))
(while (>= M D)
(if (=0 (% N D))
(setq M (sqrt (setq N (/ N (link D)))))
(inc 'D (pop 'L)) ) )
(link N) ) ) )
(de sumdigits (N)
(sum format (chop N)) )
(de smith (X)
(make
(for N X
(let R (factor N)
(and
(cdr R)
(= (sum sumdigits R) (sumdigits N))
(link N) ) ) ) ) )
(let L (smith 10000)
(println 'first-10 (head 10 L)) (println 'last-10 (tail 10 L)) (println 'all (length L)) )</lang>
- Output:
first-10 (4 22 27 58 85 94 121 166 202 265) last-10 (9843 9849 9861 9880 9895 9924 9942 9968 9975 9985) all 376
PureBasic
<lang PureBasic>DisableDebugger
- ECHO=#True ; #True: Print all results
Global NewList f.i()
Procedure.i ePotenz(Wert.i)
Define.i var=Wert, i While var i+1 var/10 Wend ProcedureReturn i
EndProcedure
Procedure.i n_Element(Wert.i,Stelle.i=1)
If Stelle>0 ProcedureReturn (Wert%Int(Pow(10,Stelle))-Wert%Int(Pow(10,Stelle-1)))/Int(Pow(10,Stelle-1)) Else ProcedureReturn 0 EndIf
EndProcedure
Procedure.i qSumma(Wert.i)
Define.i sum, pos For pos=1 To ePotenz(Wert) sum+ n_Element(Wert,pos) Next pos ProcedureReturn sum
EndProcedure
Procedure.b IsPrime(n.i)
Define.i i=5 If n<2 : ProcedureReturn #False : EndIf If n%2=0 : ProcedureReturn Bool(n=2) : EndIf If n%3=0 : ProcedureReturn Bool(n=3) : EndIf While i*i<=n If n%i=0 : ProcedureReturn #False : EndIf i+2 If n%i=0 : ProcedureReturn #False : EndIf i+4 Wend ProcedureReturn #True
EndProcedure
Procedure PFZ(n.i,pf.i=2)
If n>1 And n<>pf
If n%pf=0
AddElement(f()) : f()=pf
PFZ(n/pf,pf)
Else
While Not IsPrime(pf+1) : pf+1 : Wend
PFZ(n,pf+1)
EndIf
ElseIf n=pf
AddElement(f()) : f()=pf
EndIf
EndProcedure
OpenConsole("Smith numbers")
- upto=100
- sn=0 : Gosub Smith_loop
- upto=1000
- sn=0 : Gosub Smith_loop
upto=10000 : sn=0 : Gosub Smith_loop Input() End
Smith_loop:
For i=2 To upto
ClearList(f()) : qs=0
PFZ(i)
CompilerIf #ECHO : Print(Str(i)+~": \t") : CompilerEndIf
ForEach f()
CompilerIf #ECHO : Print(Str(F())+~"\t") : CompilerEndIf
qs+qSumma(f())
Next
If ListSize(f())>1 And qSumma(i)=qs
CompilerIf #ECHO : Print("SMITH-NUMBER") : CompilerEndIf
sn+1
EndIf
CompilerIf #ECHO : PrintN("") : CompilerEndIf
Next
Print(~"\n"+Str(sn)+" Smith number up to "+Str(upto))
Return</lang>
- Output:
. . . 9975: 3 5 5 7 19 SMITH-NUMBER 9976: 2 2 2 29 43 9977: 11 907 9978: 2 3 1663 9979: 17 587 9980: 2 2 5 499 9981: 3 3 1109 9982: 2 7 23 31 9983: 67 149 9984: 2 2 2 2 2 2 2 2 3 13 9985: 5 1997 SMITH-NUMBER 9986: 2 4993 9987: 3 3329 9988: 2 2 11 227 9989: 7 1427 9990: 2 3 3 3 5 37 9991: 97 103 9992: 2 2 2 1249 9993: 3 3331 9994: 2 19 263 9995: 5 1999 9996: 2 2 3 7 7 17 9997: 13 769 9998: 2 4999 9999: 3 3 11 101 10000: 2 2 2 2 5 5 5 5 376 Smith number up To 10000
Python
Procedural
<lang python>from sys import stdout
def factors(n):
rt = []
f = 2
if n == 1:
rt.append(1);
else:
while 1:
if 0 == ( n % f ):
rt.append(f);
n //= f
if n == 1:
return rt
else:
f += 1
return rt
def sum_digits(n):
sum = 0
while n > 0:
m = n % 10
sum += m
n -= m
n //= 10
return sum
def add_all_digits(lst):
sum = 0
for i in range (len(lst)):
sum += sum_digits(lst[i])
return sum
def list_smith_numbers(cnt):
for i in range(4, cnt):
fac = factors(i)
if len(fac) > 1:
if sum_digits(i) == add_all_digits(fac):
stdout.write("{0} ".format(i) )
- entry point
list_smith_numbers(10_000)</lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 ...
9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Functional
<lang python>Smith numbers
from itertools import dropwhile from functools import reduce from math import floor, sqrt
- isSmith :: Int -> Bool
def isSmith(n):
True if n is a Smith number.
pfs = primeFactors(n)
return (1 < len(pfs) or n != pfs[0]) and (
sumDigits(n) == reduce(
lambda a, x: a + sumDigits(x),
pfs, 0
)
)
- primeFactors :: Int -> [Int]
def primeFactors(x):
List of prime factors of x
def go(n):
fs = list(dropwhile(
mod(n),
range(2, 1 + floor(sqrt(n)))
))[0:1]
return fs + go(floor(n / fs[0])) if fs else [n] return go(x)
- sumDigits :: Int -> Int
def sumDigits(n):
The sum of the decimal digits of n
def f(x):
return Just(divmod(x, 10)) if x else Nothing()
return sum(unfoldl(f)(n))
- TEST ----------------------------------------------------
- main :: IO ()
def main():
Count and samples of Smith numbers below 10k
lowSmiths = [x for x in range(2, 10000) if isSmith(x)] lowSmithCount = len(lowSmiths)
print('\n'.join([
'Count of Smith Numbers below 10k:',
str(lowSmithCount),
'\nFirst 15 Smith Numbers:',
' '.join(str(x) for x in lowSmiths[0:15]),
'\nLast 12 Smith Numbers below 10000:',
' '.join(str(x) for x in lowSmiths[lowSmithCount - 12:])
]))
- GENERIC -------------------------------------------------
- Just :: a -> Maybe a
def Just(x):
Constructor for an inhabited Maybe (option type) value.
Wrapper containing the result of a computation.
return {'type': 'Maybe', 'Nothing': False, 'Just': x}
- Nothing :: Maybe a
def Nothing():
Constructor for an empty Maybe (option type) value.
Empty wrapper returned where a computation is not possible.
return {'type': 'Maybe', 'Nothing': True}
- mod :: Int -> Int -> Int
def mod(n):
n modulo d return lambda d: n % d
- unfoldl(lambda x: Just(((x - 1), x)) if 0 != x else Nothing())(10)
- -> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
- unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
Dual to reduce or foldl.
Where these reduce a list to a summary value, unfoldl
builds a list from a seed value.
Where f returns Just(a, b), a is appended to the list,
and the residual b is used as the argument for the next
application of f.
When f returns Nothing, the completed list is returned.
def go(v):
x, r = v, v
xs = []
while True:
mb = f(x)
if mb.get('Nothing'):
return xs
else:
x, r = mb.get('Just')
xs.insert(0, r)
return xs
return lambda x: go(x)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
Count of Smith Numbers below 10k: 376 First 15 Smith Numbers: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 Last 12 Smith Numbers below 10000: 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
Racket
<lang racket>#lang racket (require math/number-theory)
(define (sum-of-digits n)
(let inr ((n n) (s 0)) (if (zero? n) s (let-values (([q r] (quotient/remainder n 10))) (inr q (+ s r))))))
(define (smith-number? n)
(and (not (prime? n))
(= (sum-of-digits n)
(for/sum ((pe (in-list (factorize n))))
(* (cadr pe) (sum-of-digits (car pe)))))))
(module+ test
(require rackunit) (check-equal? (sum-of-digits 0) 0) (check-equal? (sum-of-digits 33) 6) (check-equal? (sum-of-digits 30) 3)
(check-true (smith-number? 166)))
(module+ main
(let loop ((ns (filter smith-number? (range 1 (add1 10000)))))
(unless (null? ns)
(let-values (([l r] (split-at ns (min (length ns) 15))))
(displayln l)
(loop r)))))</lang>
- Output:
(4 22 27 58 85 94 121 166 202 265 274 319 346 355 378) (382 391 438 454 483 517 526 535 562 576 588 627 634 636 645) (648 654 663 666 690 706 728 729 762 778 825 852 861 895 913)
…
(9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708) (9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975) (9985)
Raku
(formerly Perl 6) <lang perl6>constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime;
multi factors ( 1 ) { 1 } multi factors ( Int $remainder is copy ) {
gather for @primes -> $factor {
# if remainder < factor², we're done
if $factor * $factor > $remainder {
take $remainder if $remainder > 1;
last;
}
# How many times can we divide by this prime?
while $remainder %% $factor {
take $factor;
last if ($remainder div= $factor) === 1;
}
}
}
- Code above here is verbatim from RC:Count_in_factors#Raku
sub is_smith_number ( Int $n ) {
(!$n.is-prime) and ( [+] $n.comb ) == ( [+] factors($n).join.comb );
}
my @s = grep &is_smith_number, 2 ..^ 10_000; say "{@s.elems} Smith numbers below 10_000"; say 'First 10: ', @s[ ^10 ]; say 'Last 10: ', @s[ *-10 .. * ];</lang>
- Output:
376 Smith numbers below 10_000 First 10: (4 22 27 58 85 94 121 166 202 265) Last 10: (9843 9849 9861 9880 9895 9924 9942 9968 9975 9985)
REXX
unoptimized
<lang rexx>/*REXX program finds (and maybe displays) Smith (or joke) numbers up to a given N.*/ parse arg N . /*obtain optional argument from the CL.*/ if N== | N=="," then N=10000 /*Not specified? Then use the default.*/ tell= (N>0); N=abs(N) - 1 /*use the │N│ for computing (below).*/ w=length(N) /*W: used for aligning Smith numbers. */
- =0 /*#: Smith numbers found (so far). */
@=; do j=4 to N; /*process almost all numbers up to N. */
if sumD(j) \== sumfactr(j) then iterate /*Not a Smith number? Then ignore it.*/
#=#+1 /*bump the Smith number counter. */
if \tell then iterate /*Not showing the numbers? Keep looking*/
@=@ right(j, w); if length(@)>199 then do; say substr(@, 2); @=; end
end /*j*/ /* [↑] if N>0, then display Smith #s.*/
if @\== then say substr(@, 2) /*if any residual Smith #s, display 'em*/ say /* [↓] display the number of Smith #s.*/ say # ' Smith numbers found ≤ ' N"." /*display number of Smith numbers found*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sumD: parse arg x 1 s 2; do d=2 for length(x)-1; s=s+substr(x,d,1); end; return s /*──────────────────────────────────────────────────────────────────────────────────────*/ sumFactr: procedure; parse arg z; $=0; f=0 /*obtain the Z number. */
do while z//2==0; $=$+2; f=f+1; z=z% 2; end /*maybe add factor of 2*/
do while z//3==0; $=$+3; f=f+1; z=z% 3; end /* " " " " 3*/
/* ___*/
do j=5 by 2 while j<=z & j*j<=n /*minimum of Z or √ N */
if j//3==0 then iterate /*skip factors that ÷ 3*/
do while z//j==0; f=f+1; $=$+sumD(j); z=z%j; end /*maybe reduce Z by J */
end /*j*/ /* [↓] Z: what's left*/
if z\==1 then do; f=f+1; $=$+sumD(z); end /*Residual? Then add Z*/
if f<2 then return 0 /*Prime? Not a Smith#*/
return $ /*else return sum digs.*/</lang>
- output when using the default input:
(Shown at 2/3 size.)
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985 376 Smith numbers found ≤ 9999.
optimized
This REXX version uses a faster version of the sumFactr function; it's over 20 times faster than the
unoptimized version using a (negative) one million for N.
<lang rexx>/*REXX program finds (and maybe displays) Smith (or joke) numbers up to a given N.*/
parse arg N . /*obtain optional argument from the CL.*/
if N== | N=="," then N=10000 /*Not specified? Then use the default.*/
tell= (N>0); N=abs(N) - 1 /*use the │N│ for computing (below).*/
- =0 /*the number of Smith numbers (so far).*/
w=length(N) /*W: used for aligning Smith numbers. */ @=; do j=4 for max(0, N-3) /*process almost all numbers up to N. */
if sumD(j) \== sumFactr(j) then iterate /*Not a Smith number? Then ignore it.*/
#=#+1 /*bump the Smith number counter. */
if \tell then iterate /*Not showing the numbers? Keep looking*/
@=@ right(j, w); if length(@)>199 then do; say substr(@, 2); @=; end
end /*j*/ /* [↑] if N>0, then display Smith #s.*/
if @\== then say substr(@, 2) /*if any residual Smith #s, display 'em*/ say /* [↓] display the number of Smith #s.*/ say # ' Smith numbers found ≤ ' max(0,N)"." /*display number of Smith numbers found*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sumD: parse arg x 1 s 2; do d=2 for length(x)-1; s=s+substr(x,d,1); end; return s /*──────────────────────────────────────────────────────────────────────────────────────*/ sumFactr: procedure; parse arg z; $=0; f=0 /*obtain Z number (arg1).*/
do while z// 2==0; $=$+ 2; f=f+1; z=z% 2; end /*maybe add factor of 2. */
do while z// 3==0; $=$+ 3; f=f+1; z=z% 3; end /* " " " " 3. */
do while z// 5==0; $=$+ 5; f=f+1; z=z% 5; end /* " " " " 5. */
do while z// 7==0; $=$+ 7; f=f+1; z=z% 7; end /* " " " " 7. */
t=z; r=0; q=1; do while q<=t; q=q*4; end /*R: will be the iSqrt(Z).*/
do while q>1; q=q%4; _=t-r-q; r=r%2; if _>=0 then do; t=_; r=r+q; end
end /*while q>1*/ /* [↑] compute int. SQRT(Z)*/
do j=11 by 6 to r while j<=z /*skip factors that are ÷ 3*/
parse var j -1 _; if _\==5 then, /*is last dec. digit ¬a 5 ?*/
do while z//j==0; f=f+1; $=$+sumD(j); z=z%j; end /*maybe reduce Z by J*/
if _==3 then iterate; y=j+2
do while z//y==0; f=f+1; $=$+sumD(y); z=z%y; end /*maybe reduce Z by Y*/
end /*j*/ /* [↓] Z is what's left. */
if z\==1 then do; f=f+1; $=$+sumD(z); end /*if a residual, then add Z*/
if f<2 then return 0 /*Is prime? It's not Smith#*/
return $ /*else, return sum of digs.*/</lang>
- output when using the input of (negative) one million: -1000000
29928 Smith numbers found ≤ 999999.
Ring
<lang ring>
- Project : Smith numbers
see "All the Smith Numbers < 1000 are:" + nl
for prime = 1 to 1000
decmp = []
sum1 = sumDigits(prime)
decomp(prime)
sum2 = 0
if len(decmp)>1
for n=1 to len(decmp)
cstr = string(decmp[n])
for m= 1 to len(cstr)
sum2 = sum2 + number(cstr[m])
next
next
ok
if sum1 = sum2
see "" + prime + " "
ok
next
func decomp nr
for i = 1 to nr
if isPrime(i) and nr % i = 0
add(decmp, i)
pr = i
while true
pr = pr * i
if nr%pr = 0
add(decmp, i)
else
exit
ok
end
ok
next
func isPrime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1
func sumDigits n
sum = 0
while n > 0.5
m = floor(n / 10)
digit = n - m * 10
sum = sum + digit
n = m
end
return sum
</lang> Output:
All the Smith Numbers < 1000 are: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985
Ruby
<lang ruby>require "prime"
class Integer
def smith?
return false if prime?
digits.sum == prime_division.map{|pr,n| pr.digits.sum * n}.sum
end
end
n = 10_000 res = 1.upto(n).select(&:smith?)
puts "#{res.size} smith numbers below #{n}:
- {res.first(5).join(", ")},... #{res.last(5).join(", ")}"</lang>
- Output:
376 smith numbers below 10000: 4, 22, 27, 58, 85,... 9924, 9942, 9968, 9975, 9985
Rust
<lang Rust>fn main () {
//We just need the primes below 100
let primes = vec![2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];
let mut solution = Vec::new();
let mut number;
for i in 4..10000 {
//Factorize each number below 10.000
let mut prime_factors = Vec::new();
number = i;
for j in &primes {
while number % j == 0 {
number = number / j;
prime_factors.push(j);
}
if number == 1 { break; }
}
//Number is 1 (not a prime factor) if the factorization is complete or a prime bigger than 100
if number != 1 { prime_factors.push(&number); }
//Avoid the prime numbers
if prime_factors.len() < 2 { continue; }
//Check the smith number definition
if prime_factors.iter().fold(0, |n,x| n + x.to_string().chars().map(|d| d.to_digit(10).unwrap()).fold(0, |n,x| n + x))
== i.to_string().chars().map(|d| d.to_digit(10).unwrap()).fold(0, |n,x| n + x) {
solution.push(i);
}
}
println!("Smith numbers below 10000 ({}) : {:?}",solution.len(), solution);
}</lang>
- Output:
Smith numbers below 10000 (376) : [4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985] real 0m0.014s user 0m0.014s sys 0m0.000s
Scala
<lang Scala>object SmithNumbers extends App {
def sumDigits(_n: Int): Int = {
var n = _n
var sum = 0
while (n > 0) {
sum += (n % 10)
n /= 10
}
sum
}
def primeFactors(_n: Int): List[Int] = {
var n = _n
val result = new collection.mutable.ListBuffer[Int]
val i = 2
while (n % i == 0) {
result += i
n /= i
}
var j = 3
while (j * j <= n) {
while (n % j == 0) {
result += i
n /= j
}
j += 2
}
if (n != 1) result += n
result.toList
}
for (n <- 1 until 10000) {
val factors = primeFactors(n)
if (factors.size > 1) {
var sum = sumDigits(n)
for (f <- factors) sum -= sumDigits(f)
if (sum == 0) println(n)
}
}
}</lang>
Sidef
<lang ruby>var primes = Enumerator({ |callback|
static primes = Hash()
var p = 2
loop {
callback(p)
p = (primes{p} := p.next_prime)
}
})
func factors(remainder) {
remainder == 1 && return([remainder])
gather {
primes.each { |factor|
if (factor*factor > remainder) {
take(remainder) if (remainder > 1)
break
}
while (factor.divides(remainder)) {
take(factor)
break if ((remainder /= factor) == 1)
}
}
}
}
func is_smith_number(n) {
!n.is_prime && (n.digits.sum == factors(n).join.to_i.digits.sum)
}
var s = range(2, 10_000).grep { is_smith_number(_) } say "#{s.len} Smith numbers below 10_000" say "First 10: #{s.first(10)}" say "Last 10: #{s.last(10)}"</lang>
- Output:
376 Smith numbers below 10_000 First 10: [4, 22, 27, 58, 85, 94, 121, 166, 202, 265] Last 10: [9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]
Stata
<lang stata>function factor(_n) { n = _n a = J(14, 2, .) i = 0 if (mod(n, 2)==0) { j = 0 while (mod(n, 2)==0) { j++ n = n/2 } i++ a[i,1] = 2 a[i,2] = j } for (k=3; k*k<=n; k=k+2) { if (mod(n, k)==0) { j = 0 while (mod(n, k)==0) { j++ n = n/k } i++ a[i,1] = k a[i,2] = j } } if (n>1) { i++ a[i,1] = n a[i,2] = 1 } return(a[1::i,.]) }
function sumdigits(_n) { n = _n for (s=0; n>0; n=floor(n/10)) s = s+mod(n,10) return(s) }
function smith(n) { a = J(n, 1, .) i = 0 for (j=2; j<=n; j++) { f = factor(j) m = rows(f) if (m>1 | f[1,2]>1) { s = 0 for (k=1; k<=m; k++) s = s+sumdigits(f[k,1])*f[k,2] if (s==sumdigits(j)) a[++i] = j } } return(a[1::i]) }
a = smith(10000) n = rows(a) n
376
a[1::10]'
1 2 3 4 5 6 7 8 9 10 +-------------------------------------------------------------+ 1 | 4 22 27 58 85 94 121 166 202 265 | +-------------------------------------------------------------+
a[n-9::n]'
1 2 3 4 5 6 7 8 9 10 +-----------------------------------------------------------------------+ 1 | 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985 | +-----------------------------------------------------------------------+</lang>
Swift
<lang swift>extension BinaryInteger {
@inlinable
public var isSmith: Bool {
guard self > 3 else {
return false
}
let primeFactors = primeDecomposition()
guard primeFactors.count != 1 else {
return false
}
return primeFactors.map({ $0.sumDigits() }).reduce(0, +) == sumDigits()
}
@inlinable
public func primeDecomposition() -> [Self] {
guard self > 1 else { return [] }
func step(_ x: Self) -> Self {
return 1 + (x << 2) - ((x >> 1) << 1)
}
let maxQ = Self(Double(self).squareRoot()) var d: Self = 1 var q: Self = self & 1 == 0 ? 2 : 3
while q <= maxQ && self % q != 0 {
q = step(d)
d += 1
}
return q <= maxQ ? [q] + (self / q).primeDecomposition() : [self] }
@inlinable
public func sumDigits() -> Self {
return String(self).lazy.map({ Self(Int(String($0))!) }).reduce(0, +)
}
}
let smiths = (0..<10_000).filter({ $0.isSmith })
print("Num Smith numbers below 10,000: \(smiths.count)") print("First 10 smith numbers: \(Array(smiths.prefix(10)))") print("Last 10 smith numbers below 10,000: \(Array(smiths.suffix(10)))") </lang>
- Output:
Num Smith numbers below 10,000: 376 First 10 smith numbers: [4, 22, 27, 58, 85, 94, 121, 166, 202, 265] Last 10 smith numbers below 10,000: [9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]
Tcl
<lang Tcl>proc factors {x} {
# list the prime factors of x in ascending order
set result [list]
while {$x % 2 == 0} {
lappend result 2
set x [expr {$x / 2}]
}
for {set i 3} {$i*$i <= $x} {incr i 2} {
while {$x % $i == 0} {
lappend result $i
set x [expr {$x / $i}]
}
}
if {$x != 1} {lappend result $x}
return $result
}
proc digitsum {n} {
::tcl::mathop::+ {*}[split $n ""]
}
proc smith? {n} {
set fs [factors $n]
if {[llength $fs] == 1} {
return false ;# $n is prime
}
expr {[digitsum $n] == [digitsum [join $fs ""]]}
} proc range {n} {
for {set i 1} {$i < $n} {incr i} {lappend result $i}
return $result
}
set smiths [lmap i [range 10000] {
if {![smith? $i]} continue
set i
}]
puts [lrange $smiths 0 12]... puts ...[lrange $smiths end-12 end] puts "([llength $smiths] total)" </lang>
- Output:
4 22 27 58 85 94 121 166 202 265 274 319 346... ...9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985 (376 total)
Wren
<lang ecmascript>import "/math" for Int import "/fmt" for Fmt import "/seq" for Lst
var sumDigits = Fn.new { |n|
var sum = 0
while (n > 0) {
sum = sum + n%10
n = (n/10).floor
}
return sum
}
var smiths = [] System.print("The Smith numbers below 10,000 are:") for (i in 2...10000) {
if (!Int.isPrime(i)) {
var thisSum = sumDigits.call(i)
var factors = Int.primeFactors(i)
var factSum = factors.reduce(0) { |acc, f| acc + sumDigits.call(f) }
if (thisSum == factSum) smiths.add(i)
}
} for (chunk in Lst.chunks(smiths, 16)) Fmt.print("$4d", chunk)</lang>
- Output:
The Smith numbers below 10,000 are: 4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
zkl
Uses the code (primeFactors) from Prime decomposition#zkl. <lang zkl>fcn smithNumbers(N=0d10_000){ // -->(Smith numbers to N)
[2..N].filter(fcn(n){
(pfs:=primeFactors(n)).len()>1 and
n.split().sum(0)==primeFactors(n).apply("split").flatten().sum(0)
})
}</lang> <lang zkl>sns:=smithNumbers(); sns.toString(*).println(" ",sns.len()," numbers");</lang>
- Output:
L(4,22,27,58,85,94,121,166,202,265,274,319,346,355,378,382,391, ... 3091,3138,3168,3174,3226,3246,3258,3294,3345,3366,3390,3442,3505, ... 9942,9968,9975,9985) 376 numbers
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