Special divisors: Difference between revisions
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=={{header|J}}== |
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<lang J>([#~([:*./0=|.&.":"0@>:@I.@(0=>:@i.|])||.&.":)"0)>:i.200</lang> |
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{{out}} |
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<pre>1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199</pre> |
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=={{header|Julia}}== |
=={{header|Julia}}== |
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Revision as of 13:05, 18 June 2021
- Task
Numbers n such that reverse(d) divides reverse(n) for all divisors d of n, where n < 200
ALGOL 68
<lang algol68>BEGIN # find numbers where reverse(d) divides reverse(n) for all divisors d #
# of n #
# returns n with the digits reversed #
OP REVERSE = ( INT n )INT:
BEGIN
INT reverse := 0;
INT v := ABS n;
WHILE v > 0 DO
reverse *:= 10 +:= v MOD 10;
v OVERAB 10
OD;
reverse * SIGN n
END # REVERSE # ;
# find the numbers up to 200 #
INT rd count := 0;
FOR n TO 199 DO
INT reverse n = REVERSE n;
BOOL reverse divisor := TRUE;
FOR d FROM 2 TO n OVER 2 WHILE reverse divisor DO
IF n MOD d = 0 THEN
# have a divisor of n #
reverse divisor := reverse n MOD REVERSE d = 0
FI
OD;
IF reverse divisor THEN
# all the divisors of n reversed divide n reversed #
print( ( " ", whole( n, -3 ) ) );
IF ( rd count +:= 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline, "Found ", whole( rd count, 0 ), " ""special divisors"" below 200", newline ) )
END</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 "special divisors" below 200
ALGOL W
<lang algolw>begin % find numbers where reverse(d) divides reverse(n) for all divisors d %
% of n %
% returns n with the digits reversed %
integer procedure reverse ( integer value n ) ;
begin
integer r, v;
r := 0;
v := abs n;
while v > 0 do begin
r := ( r * 10 ) + ( v rem 10 );
v := v div 10
end while_v_gt_0 ;
if n < 0 then - r else r
end reverse ;
% find the numbers up to 200 %
integer rdCount;
rdCount := 0;
for n := 1 until 199 do begin
integer reverseN, d, maxD;
logical reverseDivisor;
reverseN := reverse( n );
reverseDivisor := true;
d := 1;
maxD := n div 2;
while begin
d := d + 1;
d <= maxD and reverseDivisor
end
do begin
if n rem d = 0 then begin
% have a divisor of n %
reverseDivisor := reverseN rem reverse( d ) = 0
end if_n_rem_d_eq_0
end while_d_le_maxD_and_reverseDivisor ;
if reverseDivisor then begin
% all the divisors of n reversed divide n reversed %
writeon( i_w := 3, s_w := 0, " ", n );
rdCount := rdCount + 1;
if rdCount rem 10 = 0 then write()
end if_reverseDivisor
end for_n ;
write( i_w := 1, s_w := 0, "Found ", rdCount, " ""special divisors"" below 200" )
end.</lang>
- Output:
Same as the Algol 68 sample.
APL
<lang APL>(⊢(/⍨)(0∧.=(⍎⌽∘⍕)¨∘(⍸0=⍳|⊢)|(⍎⌽∘⍕))¨) ⍳200</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47
53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101
103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169
173 179 181 187 191 193 197 199
AppleScript
<lang applescript>on factors(n)
set output to {}
if (n > 0) then
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set end of output to limit
set limit to limit - 1
end if
repeat with i from limit to 1 by -1
if (n mod i is 0) then
set beginning of output to i
set end of output to n div i
end if
end repeat
end if
return output
end factors
on reversedIntVal(n, base)
set r to n mod base as integer
set n to n div base
repeat until (n = 0)
set r to r * base + n mod base
set n to n div base
end repeat
return r
end reversedIntVal
on hasSpecialDivisors(n, base)
set divisors to factors(n)
if (divisors is {}) then return false
set r to reversedIntVal(n, base)
repeat with d in divisors
if (r mod (reversedIntVal(d, base)) > 0) then return false
end repeat
return true
end hasSpecialDivisors
local output, base, n set output to {} set base to 10 repeat with n from 1 to 199
if (hasSpecialDivisors(n, base)) then set end of output to n
end repeat return {|count|:(count output), finds:output}</lang>
- Output:
<lang applescript>{|count|:72, finds:{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199}}</lang>
Delphi
<lang Delphi>program Special_Divisors; {$IFDEF FPC}
{$MODE DELPHI}
uses
SysUtils,
StrUtils;
{$ELSE}
{$APPTYPE CONSOLE}
uses
System.SysUtils,
System.StrUtils;
{$ENDIF}
const
limit1 = 200;
var
row, num, revNum, revDiv: Integer; flag: boolean;
procedure Main(); var
n,m: NativeUint;
begin
writeln('Working...'#10);
row := 0;
num := 0;
for n := 1 to limit1 do
begin
flag := True;
revNum := reversestring(n.ToString).ToInteger;
for m := 1 to n div 2 do
begin
revDiv := reversestring(m.ToString).ToInteger;
if n mod m = 0 then
if revNum mod revDiv = 0 then
flag := True
else
begin
flag := False;
Break;
end;
end;
if flag then
begin
inc(num);
inc(row);
write(n: 4);
if row mod 10 = 0 then
Writeln;
end;
end;
writeln(#10#10'Found ', num, ' special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200');
writeln('Done...');
end;
begin
Main;
{$IFNDEF UNIX} readln; {$ENDIF}
end.</lang>
- Output:
Working... 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 Done...
Factor
<lang factor>USING: grouping kernel math.functions math.parser math.primes.factors math.ranges prettyprint sequences ;
- reverse-number ( n -- reversed ) 10 >base reverse dec> ;
- special? ( n -- ? )
[ reverse-number ] [ divisors ] bi [ reverse-number divisor? ] with all? ;
200 [1..b] [ special? ] filter 18 group simple-table.</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
J
<lang J>([#~([:*./0=|.&.":"0@>:@I.@(0=>:@i.|])||.&.":)"0)>:i.200</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Julia
<lang julia>using Primes
function divisors(n)
f = [one(n)]
for (p,e) in factor(n)
f = reduce(vcat, [f*p^j for j in 1:e], init=f)
end
return f[1:end-1]
end
function isspecialdivisor(n)::Bool
isprime(n) && return true
nreverse = evalpoly(10, reverse(digits(n)))
for d in divisors(n)
dreverse = evalpoly(10, reverse(digits(d)))
!(nreverse ÷ dreverse ≈ nreverse / dreverse) && return false
end
return true
end
const specials = filter(isspecialdivisor, 1:200) foreach(p -> print(rpad(p[2], 4), p[1] % 18 == 0 ? "\n" : ""), enumerate(specials))
</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Nim
<lang Nim>import strutils
func reversed(n: Positive): int =
var n = n.int while n != 0: result = 10 * result + n mod 10 n = n div 10
func divisors(n: Positive): seq[int] =
result = @[1, n]
var d = 2
while d * d <= n:
if n mod d == 0:
result.add d
if d * d != n:
result.add n div d
inc d
var count = 0 for n in 1..<200:
let revn = reversed(n)
block check:
for d in divisors(n):
if revn mod reversed(d) != 0:
break check
inc count
stdout.write ($n).align(3), if count mod 12 == 0: '\n' else: ' '</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Pascal
see http://rosettacode.org/wiki/Special_Divisors#Delphi%7CDelphi
Perl
<lang perl>use strict; use warnings; use feature 'say'; use ntheory 'divisors';
my @sd; for my $n (1..199) {
map { next if $_ != int $_ } map { reverse($n) / reverse $_ } divisors $n;
push @sd, $n;
}
say @sd . " matching numbers:\n" .
(sprintf "@{['%4d' x @sd]}", @sd) =~ s/(.{40})/$1\n/gr;</lang>
- Output:
72 matching numbers: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Phix
function rev(integer n) integer r = 0 while n do r = r*10+remainder(n,10) n = floor(n/10) end while return r end function function special_divisors(integer n) sequence fn = factors(n) if length(fn) then integer rn = rev(n) for i=1 to length(fn) do if remainder(rn,rev(fn[i])) then return false end if end for end if return true end function sequence res = apply(true,sprintf,{{"%3d"},filter(tagset(200),special_divisors)}) printf(1,"Found %d special divisors:\n%s\n",{length(res),join_by(res,1,18)})
- Output:
Found 72 special divisors: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Raku
<lang perl6>use Prime::Factor:ver<0.3.0+>;
say "{+$_} matching numbers:\n{.batch(10)».fmt('%3d').join: "\n"}"
given (1..^200).grep: { all .flip «%%« .&divisors».flip };</lang>
- Output:
72 matching numbers: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
REXX
<lang rexx>/*REXX program finds special divisors: numbers N such that reverse(D) divides ··· */ /*────────────────────────── reverse(N) for all divisors D of N, where N < 200. */ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 200 /* " " " " " " */ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= 10 /*width of a number in any column. */ title= ' special divisors N that reverse(D) divides reverse(N) for all divisiors' ,
' D of N, where N < ' commas(hi)
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') found= 0; idx= 1 /*initialize # found numsers and index.*/ $= /*a list of numbers found (so far). */
do j=1 for hi-1; r= reverse(j) /*search for special divisors. */
do k=2 to j%2 /*skip the first divisor (unity) & last*/
if j//k==0 then if r//reverse(k)\==0 then iterate J /*Not OK? Skip*/
end /*m*/
found= found+1 /*bump the number of special divisors. */
if cols<0 then iterate /*Build the list (to be shown later)? */
c= commas(j) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a special div ─► list, allow big#*/
if found//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') say say 'Found ' commas(found) title exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>
- output when using the default inputs:
index │ special divisors N that reverse(D) divides reverse(N) for all divisiors D of N, where N < 200 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 1 2 3 4 5 6 7 8 9 11 11 │ 13 17 19 22 23 26 27 29 31 33 21 │ 37 39 41 43 44 46 47 53 55 59 31 │ 61 62 66 67 69 71 73 77 79 82 41 │ 83 86 88 89 93 97 99 101 103 107 51 │ 109 113 121 127 131 137 139 143 149 151 61 │ 157 163 167 169 173 179 181 187 191 193 71 │ 197 199 ───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 72 special divisors N that reverse(D) divides reverse(N) for all divisiors D of N, where N < 200
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl
row = 0 num = 0 limit1 = 200
for n = 1 to limit1
flag = 1
revNum = rever(string(n))
revNum = number(revNum)
for m = 1 to n/2
revDiv = rever(String(m))
revDiv = number(revDiv)
if n%m = 0
if revNum % revDiv = 0
flag = 1
else
flag = 0
exit
ok
ok
next
if flag = 1
num = num + 1
row = row + 1
see "" + n + " "
if row%10 = 0
see nl
ok
ok
next
see nl + "Found " + num + " special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200" + nl see "done..." + nl
func rever(str)
rev = ""
for n = len(str) to 1 step -1
rev = rev + str[n]
next
return rev
</lang>
- Output:
working... 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 done...
Wren
<lang ecmascript>import "/math" for Int import "/seq" for Lst import "/fmt" for Fmt
var reversed = Fn.new { |n|
var rev = 0
while (n > 0) {
rev = rev * 10 + n % 10
n = (n/10).floor
}
return rev
}
var special = [] for (n in 1...200) {
var divs = Int.divisors(n)
var revN = reversed.call(n)
if (divs.all { |d| revN % reversed.call(d) == 0 }) special.add(n)
} System.print("Special divisors in the range 0..199:") for (chunk in Lst.chunks(special, 12)) Fmt.print("$3d", chunk) System.print("\n%(special.count) special divisors found.")</lang>
- Output:
Special divisors in the range 0..199: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 special divisors found.
XPL0
<lang XPL0>func Reverse(N); \Reverse the order of the digits int N, M; [M:= 0; repeat N:= N/10;
M:= M*10 + rem(0);
until N = 0; return M; ];
func Test(N); \Return 'true' if reverse(D) divides reverse(N) for all divisors D of N int N, D, RevNum, RevDiv; [RevNum:= Reverse(N); for D:= 1 to N/2 do
if rem(N/D) = 0 then
[RevDiv:= Reverse(D);
if rem(RevNum/RevDiv) then return false;
];
return true; ];
int Count, N; [Count:= 0; for N:= 1 to 199 do
[if Test(N) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
];
];
CrLf(0); IntOut(0, Count); Text(0, " such numbers found."); ]</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 such numbers found.