Duffinian numbers: Difference between revisions
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</pre>
=={{header|APL}}==
<syntaxhighlight lang="apl">duffinian_numbers←{
sigma ← +/(⍸0=⍳|⊢)
duff ← sigma((1=∨)∧⊣>1+⊢)⊢
⎕←'First 50 Duffinian numbers:'
⎕←5 10⍴(⊢(/⍨)duff¨)⍳220
⎕←'First 15 Duffinian triplets:'
⎕←(0 1 2∘.+⍨⊢(/⍨)0 1 2(⊃∧.⌽)(⊂duff¨))⍳8500
}</syntaxhighlight>
{{out}}
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 15 Duffinian triplets:
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451</pre>
=={{header|AppleScript}}==
As is often the case with these tasks, it takes as much code to format the output as it does to get the numbers. :)
Line 301 ⟶ 333:
[1443 1444 1445] [2303 2304 2305] [2449 2450 2451] [3599 3600 3601] [3871 3872 3873]
[5183 5184 5185] [5617 5618 5619] [6049 6050 6051] [6399 6400 6401] [8449 8450 8451]</pre>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="basic"> 100 DEF FN MOD(NUM) = NUM - INT (NUM / DIV) * DIV: REM NUM MOD DIV
110 M = 50:N = 4
120 PRINT "FIRST "M" DUFFINIAN NUMBERS:"
130 FOR C = 0 TO M STEP 0
140 GOSUB 600"DUFF
150 IF DUFF THEN PRINT RIGHT$ (" " + STR$ (N),4);:C = C + 1
160 N = N + 1
170 NEXT C
180 M = 15:S = 4:M$ = CHR$ (13)
190 PRINT M$M$"FIRST "M" DUFFINIAN TRIPLETS:"
200 FOR C = 0 TO M STEP 0
210 FOR D = 2 TO 0 STEP - 1:N = S + D: GOSUB 600: IF DUFF THEN NEXT D
220 IF D < 0 THEN C = C + 1: PRINT RIGHT$ (" " + STR$ (S) + "-",5) LEFT$ ( STR$ (S + 2) + " ",5);:D = 0
230 S = S + D + 1
240 NEXT C
250 END
REM ISPRIME V RETURNS ISPRIME
260 ISPRIME = FALSE: IF V < 2 THEN RETURN
270 DIV = 2:ISPRIME = FN MOD(V): IF NOT ISPRIME THEN ISPRIME = V = 2: RETURN
280 LIMIT = SQR (V): IF LIMIT > = 3 THEN FOR DIV = 3 TO LIMIT STEP 2:ISPRIME = FN MOD(V): IF ISPRIME THEN NEXT DIV
290 RETURN
REM GREATEST COMMON DIVISOR (GCD) A B RETURNS GCD
300 A = ABS ( INT (A))
310 B = ABS ( INT (B))
320 GCD = A * NOT NOT B
330 FOR B = B + A * NOT B TO 0 STEP 0
340 A = GCD
350 GCD = B
360 B = A - INT (A / GCD) * GCD
370 NEXT B
380 RETURN
REM SUMDIV NUM RETURNS SUM
400 DIV = 2
410 SUM = 0
420 QUOT = NUM / DIV
430 IF DIV > QUOT THEN SUM = 1: RETURN
440 FOR LOOP = 0 TO 1 STEP 0
450 IF FN MOD(NUM) = 0 THEN SUM = SUM + DIV: IF DIV < > QUOT THEN SUM = SUM + QUOT
460 DIV = DIV + 1
470 QUOT = NUM / DIV
480 LOOP = DIV > QUOT
500 NEXT LOOP
510 SUM = SUM + 1
520 RETURN
REM DUFF N RETURNS DUFF
600 DUFF = FALSE
610 V = N: GOSUB 260"ISPRIME
620 IF ISPRIME THEN RETURN
630 NUM = N: GOSUB 400"SUMDIV
640 A = SUM:B = N: GOSUB 300"GCD
650 DUFF = GCD = 1
660 RETURN</syntaxhighlight>
{{out}}
<pre>FIRST 50 DUFFINIAN NUMBERS:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77 81 85 93 98 100 111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217
FIRST 15 DUFFINIAN TRIPLETS:
63-65 323-325 511-513 721-723 899-901 1443-1445 2303-2305 2449-2451 3599-3601 3871-3873 5183-5185 5617-5619 6049-6051 6399-6401 8449-8451
</pre>
==={{header|FreeBASIC}}===
{{trans|XPL0}}
<syntaxhighlight lang="vb">#include "isprime.bas"
Function GCD(p As Integer, q As Integer) As Integer
Return Iif(q = 0, p, GCD(q, p Mod q))
End Function
Function SumDiv(Num As Uinteger) As Uinteger
Dim As Uinteger Div = 2, Sum = 0, Quot
Do
Quot = Num / Div
If Div > Quot Then Exit Do
If Num Mod Div = 0 Then
Sum += Div
If Div <> Quot Then Sum += Quot
End If
Div += 1
Loop
Return Sum+1
End Function
Function Duff(N As Uinteger) As Boolean
Return Iif(isPrime(N), False, GCD(SumDiv(N), N) = 1)
End Function
Dim As Integer C = 0, N = 4
Print "First 50 Duffinian numbers:"
Do
If Duff(N) Then
Print Using "####"; N;
C += 1
If C Mod 20 = 0 Then Print
End If
N += 1
Loop Until C >= 50
C = 0 : N = 4
Print !"\n\nFirst 50 Duffinian triplets:"
Do
If Duff(N) And Duff(N+1) And Duff(N+2) Then
Print Using !" [###### ###### ######]\t"; N; N+1; N+2;
C += 1
If C Mod 4 = 0 Then Print
End If
N += 1
Loop Until C >= 50
Sleep</syntaxhighlight>
{{out}}
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125 128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 50 Duffinian triplets:
[ 63 64 65] [ 323 324 325] [ 511 512 513] [ 721 722 723]
[ 899 900 901] [ 1443 1444 1445] [ 2303 2304 2305] [ 2449 2450 2451]
[ 3599 3600 3601] [ 3871 3872 3873] [ 5183 5184 5185] [ 5617 5618 5619]
[ 6049 6050 6051] [ 6399 6400 6401] [ 8449 8450 8451] [ 10081 10082 10083]
[ 10403 10404 10405] [ 11663 11664 11665] [ 12481 12482 12483] [ 13447 13448 13449]
[ 13777 13778 13779] [ 15841 15842 15843] [ 17423 17424 17425] [ 19043 19044 19045]
[ 26911 26912 26913] [ 30275 30276 30277] [ 36863 36864 36865] [ 42631 42632 42633]
[ 46655 46656 46657] [ 47523 47524 47525] [ 53137 53138 53139] [ 58563 58564 58565]
[ 72961 72962 72963] [ 76175 76176 76177] [ 79523 79524 79525] [ 84099 84100 84101]
[ 86527 86528 86529] [ 94177 94178 94179] [108899 108900 108901] [121103 121104 121105]
[125315 125316 125317] [128017 128018 128019] [129599 129600 129601] [137287 137288 137289]
[144399 144400 144401] [144721 144722 144723] [154567 154568 154569] [158403 158404 158405]
[166463 166464 166465] [167041 167042 167043]</pre>
=={{header|BCPL}}==
<syntaxhighlight lang="bcpl">get "libhdr"
let calcsigmas(sig, n) be
$( sig!0 := 0
for i = 0 to n do sig!i := 0
for i = 1 to n/2 do
$( let j = i
while 0 < j <= n do
$( sig!j := sig!j + i
j := j + i
$)
$)
$)
let gcd(m, n) = n=0 -> m, gcd(n, m rem n)
let duff(sig, n) = sig!n > n+1 & gcd(n, sig!n) = 1
let triple(sig, n) = duff(sig, n) & duff(sig, n+1) & duff(sig, n+2)
let first(sig, f, max, cb) be
$( let n = 0
for i = 1 to max
$( n := n+1 repeatuntil f(sig, n)
cb(i, n)
$)
$)
let start() be
$( let showsingle(i, n) be
$( writef("%I4", n)
if i rem 10=0 then wrch('*N')
$)
let showtriple(i, n) be writef("%I2: %I6 %I6 %I6*N", i, n, n+1, n+2)
let sig = getvec(20000)
calcsigmas(sig, 20000)
writes("First 50 Duffinian numbers:*N")
first(sig, duff, 50, showsingle)
writes("*NFirst 15 Duffinian triples:*N")
first(sig, triple, 15, showtriple)
freevec(sig)
$)</syntaxhighlight>
{{out}}
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 15 Duffinian triples:
1: 63 64 65
2: 323 324 325
3: 511 512 513
4: 721 722 723
5: 899 900 901
6: 1443 1444 1445
7: 2303 2304 2305
8: 2449 2450 2451
9: 3599 3600 3601
10: 3871 3872 3873
11: 5183 5184 5185
12: 5617 5618 5619
13: 6049 6050 6051
14: 6399 6400 6401
15: 8449 8450 8451</pre>
=={{header|C++}}==
Line 377 ⟶ 616:
(166463, 166464, 166465) (167041, 167042, 167043)
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
{These subroutines would normally be in a library, but is included here for clarity}
function GetAllProperDivisors(N: Integer;var IA: TIntegerDynArray): integer;
{Make a list of all the "proper dividers" for N}
{Proper dividers are the of numbers the divide evenly into N}
var I: integer;
begin
SetLength(IA,0);
for I:=1 to N-1 do
if (N mod I)=0 then
begin
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=I;
end;
Result:=Length(IA);
end;
function GetAllDivisors(N: Integer;var IA: TIntegerDynArray): integer;
{Make a list of all the "proper dividers" for N, Plus N itself}
begin
Result:=GetAllProperDivisors(N,IA)+1;
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=N;
end;
function IsDuffinianNumber(N: integer): boolean;
{Test number to see if it a Duffinian number}
var Facts1,Facts2: TIntegerDynArray;
var Sum,I,J: integer;
begin
Result:=False;
{Must be a composite number}
if IsPrime(N) then exit;
{Get all divisors}
GetAllDivisors(N,Facts1);
{Get sum of factors}
Sum:=0;
for I:=0 to High(Facts1) do
Sum:=Sum+Facts1[I];
{Get all factor of Sum}
GetAllDivisors(Sum,Facts2);
{Test if the two number share any factors}
for I:=1 to High(Facts1) do
for J:=1 to High(Facts2) do
if Facts1[I]=Facts2[J] then exit;
{If not, they are relatively prime}
Result:=True;
end;
procedure ShowDuffinianNumbers(Memo: TMemo);
var N,Cnt,D1,D2,D3: integer;
var S: string;
begin
Cnt:=0;
S:='';
Memo.Lines.Add('First 50 Duffinian Numbers');
for N:=2 to high(integer) do
if IsDuffinianNumber(N) then
begin
Inc(Cnt);
S:=S+Format('%5d',[N]);
if (Cnt mod 10)=0 then S:=S+CRLF;
if Cnt>=50 then break;
end;
Memo.Lines.Add(S);
D1:=0; D2:=-10; D3:=0;
S:=''; Cnt:=0;
Memo.Lines.Add('First 15 Duffinian Triples');
for N:=2 to high(integer) do
if IsDuffinianNumber(N) then
begin
D1:=D2; D2:=D3;
D3:=N;
if ((D2-D1)=1) and ((D3-D2)=1) then
begin
Inc(Cnt);
S:=S+Format('(%5d%5d%5d) ',[D1,D2,D3]);
if (Cnt mod 3)=0 then S:=S+CRLF;
if Cnt>=15 then break;
end;
end;
Memo.Lines.Add(S);
end;
</syntaxhighlight>
{{out}}
<pre>
First 50 Duffinian Numbers
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 20 Duffinian Triples
( 63 64 65) ( 323 324 325) ( 511 512 513)
( 721 722 723) ( 899 900 901) ( 1443 1444 1445)
( 2303 2304 2305) ( 2449 2450 2451) ( 3599 3600 3601)
( 3871 3872 3873) ( 5183 5184 5185) ( 5617 5618 5619)
( 6049 6050 6051) ( 6399 6400 6401) ( 8449 8450 8451)
( 10081 10082 10083) ( 10403 10404 10405) ( 11663 11664 11665)
( 12481 12482 12483) ( 13447 13448 13449)
Elapsed Time: 825.340 ms.
</pre>
=={{header|Draco}}==
<syntaxhighlight lang="draco">word MAXSIGMA = 10000;
[MAXSIGMA+1]word sigma;
proc calcsigma() void:
word i, j;
for i from 0 upto MAXSIGMA do sigma[i] := 0 od;
for i from 1 upto MAXSIGMA do
for j from i by i upto MAXSIGMA do
sigma[j] := sigma[j] + i
od
od
corp
proc gcd(word a, b) word:
word c;
while b > 0 do
c := a % b;
a := b;
b := c;
od;
a
corp
proc duff(word n) bool:
sigma[n] > n+1 and gcd(n, sigma[n]) = 1
corp
proc triplet(word n) bool:
duff(n) and duff(n+1) and duff(n+2)
corp
proc first(word n; proc(word n)bool pred; proc(word i,n)void cb) void:
word i, cur;
cur := 0;
for i from 1 upto n do
while cur := cur + 1; not pred(cur) do od;
cb(i, cur)
od
corp
proc tablenum(word i, n) void:
write(n:5);
if i%10 = 0 then writeln() fi
corp
proc tripletline(word i, n) void:
writeln(i:2, ' ', n:6, n+1:6, n+2:6)
corp
proc main() void:
calcsigma();
writeln("First 50 Duffinian numbers:");
first(50, duff, tablenum);
writeln();
writeln("First 15 Duffinian triplets:");
first(15, triplet, tripletline)
corp</syntaxhighlight>
{{out}}
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 15 Duffinian triplets:
1 63 64 65
2 323 324 325
3 511 512 513
4 721 722 723
5 899 900 901
6 1443 1444 1445
7 2303 2304 2305
8 2449 2450 2451
9 3599 3600 3601
10 3871 3872 3873
11 5183 5184 5185
12 5617 5618 5619
13 6049 6050 6051
14 6399 6400 6401
15 8449 8450 8451</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
func gcd a b .
while b <> 0
h = b
b = a mod b
a = h
.
return a
.
func sumdiv num .
d = 2
repeat
quot = num div d
until d > quot
if num mod d = 0
sum += d
if d <> quot
sum += quot
.
.
d += 1
.
return sum + 1
.
func isduff n .
if isprim n = 0 and gcd sumdiv n n = 1
return 1
.
return 0
.
proc duffs . .
print "First 50 Duffinian numbers:"
n = 4
repeat
if isduff n = 1
write n & " "
cnt += 1
.
until cnt = 50
n += 1
.
cnt = 0
n = 4
print "\n\nFirst 15 Duffinian triplets:"
repeat
if isduff n = 1 and isduff (n + 1) = 1 and isduff (n + 2) = 1
print n & " - " & n + 2
cnt += 1
.
until cnt = 15
n += 1
.
.
duffs
</syntaxhighlight>
=={{header|Factor}}==
Line 423 ⟶ 934:
6399 6400 6401
8449 8450 8451
</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
local fn IsPrime( n as NSUInteger ) as BOOL
BOOL isPrime = YES
NSUInteger i
if n < 2 then exit fn = NO
if n = 2 then exit fn = YES
if n mod 2 == 0 then exit fn = NO
for i = 3 to int(n^.5) step 2
if n mod i == 0 then exit fn = NO
next
end fn = isPrime
local fn GCD( a as long, b as long ) as long
long r
if ( a == 0 ) then r = b else r = fn GCD( b mod a, a )
end fn = r
local fn SumDiv( num as NSUInteger ) as NSUInteger
NSUInteger div = 2, sum = 0, quot, result
while (1)
quot = num / div
if ( div > quot ) then result = 0 : exit while
if ( num mod div == 0 )
sum += div
if ( div != quot ) then sum += quot
end if
div++
wend
result = sum + 1
end fn = result
local fn IsDuffinian( n as NSUInteger) as BOOL
BOOL result = NO
if ( fn IsPrime(n) == NO && fn GCD( fn SumDiv(n), n ) == 1 ) then exit fn = YES
end fn = result
local fn FindDuffinians
long c = 0, n = 4
print "First 50 Duffinian numbers:"
do
if ( fn IsDuffinian(n) )
printf @"%4d \b", n
c++
if ( c mod 10 == 0 ) then print
end if
n++
until ( c >= 50 )
c = 0 : n = 4
printf @"\n\nFirst 56 Duffinian triplets:"
do
if ( fn IsDuffinian(n) and fn IsDuffinian(n + 1) and fn IsDuffinian(n + 2) )
printf @" [%6ld %6ld %6ld] \b", n, n+1, n+2
c++
if ( c mod 4 == 0 ) then print
end if
n++
until ( c >= 56 )
end fn
CFTimeInterval t
t = fn CACurrentMediaTime
fn FindDuffinians
printf @"\nCompute time: %.3f ms",(fn CACurrentMediaTime-t)*1000
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 56 Duffinian triplets:
[ 63 64 65] [ 323 324 325] [ 511 512 513] [ 721 722 723]
[ 899 900 901] [ 1443 1444 1445] [ 2303 2304 2305] [ 2449 2450 2451]
[ 3599 3600 3601] [ 3871 3872 3873] [ 5183 5184 5185] [ 5617 5618 5619]
[ 6049 6050 6051] [ 6399 6400 6401] [ 8449 8450 8451] [ 10081 10082 10083]
[ 10403 10404 10405] [ 11663 11664 11665] [ 12481 12482 12483] [ 13447 13448 13449]
[ 13777 13778 13779] [ 15841 15842 15843] [ 17423 17424 17425] [ 19043 19044 19045]
[ 26911 26912 26913] [ 30275 30276 30277] [ 36863 36864 36865] [ 42631 42632 42633]
[ 46655 46656 46657] [ 47523 47524 47525] [ 53137 53138 53139] [ 58563 58564 58565]
[ 72961 72962 72963] [ 76175 76176 76177] [ 79523 79524 79525] [ 84099 84100 84101]
[ 86527 86528 86529] [ 94177 94178 94179] [108899 108900 108901] [121103 121104 121105]
[125315 125316 125317] [128017 128018 128019] [129599 129600 129601] [137287 137288 137289]
[144399 144400 144401] [144721 144722 144723] [154567 154568 154569] [158403 158404 158405]
[166463 166464 166465] [167041 167042 167043] [175231 175232 175233] [177607 177608 177609]
[181475 181476 181477] [186623 186624 186625] [188497 188498 188499] [197191 197192 197193]
Compute time: 2963.753 ms
</pre>
Line 538 ⟶ 1,151:
6399 6400 6401
8449 8450 8451</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.Arrays;
public final class DuffianNumbers {
public static void main(String[] aArgs) {
int[] duffians = createDuffians(11_000);
System.out.println("The first 50 Duffinian numbers:");
int count = 0;
int n = 1;
while ( count < 50 ) {
if ( duffians[n] > 0 ) {
System.out.print(String.format("%4d%s", n, ( ++count % 25 == 0 ? "\n" : "" )));
}
n += 1;
}
System.out.println();
System.out.println("The first 16 Duffinian triplets:");
count = 0;
n = 3;
while( count < 16 ) {
if ( duffians[n - 2] > 0 && duffians[n - 1] > 0 && duffians[n] > 0 ) {
System.out.print(String.format("%22s%s",
"(" + ( n - 2 ) + ", " + ( n - 1 ) + ", " + n + ")", ( ++count % 4 == 0 ? "\n" : "" )));
}
n += 1;
}
System.out.println();
}
private static int[] createDuffians(int aLimit) {
// Create a list where list[i] is the divisor sum of i.
int[] result = new int[aLimit];
Arrays.fill(result, 1);
for ( int i = 2; i < aLimit; i++ ) {
for ( int j = i; j < aLimit; j += i ) {
result[j] += i;
}
}
// Set the divisor sum of non-Duffinian numbers to 0.
result[1] = 0; // 1 is not a Duffinian number.
for ( int n = 2; n < aLimit; n++ ) {
int resultN = result[n];
if ( resultN == n + 1 || gcd(n, resultN) != 1 ) {
// n is prime, or it is not relatively prime to its divisor sum.
result[n] = 0;
}
}
return result;
}
private static int gcd(int aOne, int aTwo) {
if ( aTwo == 0 ) {
return aOne;
}
return gcd(aTwo, aOne % aTwo);
}
}
</syntaxhighlight>
{{ out }}
<pre>
The first 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77 81 85 93 98 100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217
The first 16 Duffinian triplets:
(63, 64, 65) (323, 324, 325) (511, 512, 513) (721, 722, 723)
(899, 900, 901) (1443, 1444, 1445) (2303, 2304, 2305) (2449, 2450, 2451)
(3599, 3600, 3601) (3871, 3872, 3873) (5183, 5184, 5185) (5617, 5618, 5619)
(6049, 6050, 6051) (6399, 6400, 6401) (8449, 8450, 8451) (10081, 10082, 10083)
</pre>
=={{header|jq}}==
Line 554 ⟶ 1,244:
| . == ($sqrt | .*.);
# Input: a positive integer
#
# $a[$i] is $i if $i is prime, and false otherwise.
def primeSieve:
# erase(i) sets .[i*j] to false for integral j > 1
def erase($i):
if .[$i] then
reduce (range(2*$i;
else .
end;
Line 701 ⟶ 1,392:
Number of triplets: 50
</pre>
=={{header|Julia}}==
Line 755 ⟶ 1,445:
8449 8450 8451
</pre>
=={{header|MAD}}==
<syntaxhighlight lang="mad"> NORMAL MODE IS INTEGER
DIMENSION SIGMA(10000),OUTROW(10)
INTERNAL FUNCTION(AA,BB)
ENTRY TO GCD.
A = AA
B = BB
STEP WHENEVER A.E.B, FUNCTION RETURN A
WHENEVER A.G.B, A = A-B
WHENEVER A.L.B, B = B-A
TRANSFER TO STEP
END OF FUNCTION
INTERNAL FUNCTION(N)
ENTRY TO DUFF.
SIG = SIGMA(N)
FUNCTION RETURN SIG.G.N+1 .AND. GCD.(N,SIG).E.1
END OF FUNCTION
INTERNAL FUNCTION(N)
ENTRY TO TRIP.
FUNCTION RETURN DUFF.(N) .AND.
0 DUFF.(N+1) .AND. DUFF.(N+2)
END OF FUNCTION
THROUGH SZERO, FOR I=1, 1, I.G.10000
SZERO SIGMA(I) = 0
THROUGH SCALC, FOR I=1, 1, I.G.10000
THROUGH SCALC, FOR J=I, I, J.G.10000
SCALC SIGMA(J) = SIGMA(J) + I
PRINT COMMENT $ FIRST 50 DUFFINIAN NUMBERS$
CAND = 0
THROUGH DUFROW, FOR R=0, 1, R.GE.5
THROUGH DUFCOL, FOR C=0, 1, C.GE.10
SCHDUF THROUGH SCHDUF, FOR CAND=CAND+1, 1, DUFF.(CAND)
DUFCOL OUTROW(C) = CAND
DUFROW PRINT FORMAT ROWFMT,OUTROW(0),OUTROW(1),OUTROW(2),
0 OUTROW(3),OUTROW(4),OUTROW(5),OUTROW(6),
1 OUTROW(7),OUTROW(8),OUTROW(9)
PRINT COMMENT $ $
PRINT COMMENT $ FIRST 15 DUFFINIAN TRIPLETS$
CAND = 0
THROUGH DUFTRI, FOR S=0, 1, S.GE.15
SCHTRP THROUGH SCHTRP, FOR CAND=CAND+1, 1, TRIP.(CAND)
DUFTRI PRINT FORMAT TRIFMT,CAND,CAND+1,CAND+2
VECTOR VALUES ROWFMT = $10(I5)*$
VECTOR VALUES TRIFMT = $3(I7)*$
END OF PROGRAM</syntaxhighlight>
{{out}}
<pre>FIRST 50 DUFFINIAN NUMBERS
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
FIRST 15 DUFFINIAN TRIPLETS
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
Line 795 ⟶ 1,562:
991231-991233</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
/* Predicate functions that checks wether an integer is a Duffinian number or not */
duffinianp(n):=if n#1 and not primep(n) and gcd(n,divsum(n))=1 then true$
/* Function that returns a list of the first len Duffinian numbers */
duffinian_count(len):=block(
[i:1,count:0,result:[]],
while count<len do (if duffinianp(i) then (result:endcons(i,result),count:count+1),i:i+1),
result)$
/* Function that returns a list of the first len Duffinian triples */
duffinian_triples_count(len):=block(
[i:1,count:0,result:[]],
while count<len do (if map(duffinianp,[i,i+1,i+2])=[true,true,true] then (result:endcons([i,i+1,i+2],result),count:count+1),i:i+1),
result)$
/* Test cases */
/* First 50 Duffinian numbers */
duffinian_count(50);
/* First 15 Duffinian triples */
duffinian_triples_count(15);
</syntaxhighlight>
{{out}}
<pre>
[4,8,9,16,21,25,27,32,35,36,39,49,50,55,57,63,64,65,75,77,81,85,93,98,100,111,115,119,121,125,128,129,133,143,144,155,161,169,171,175,183,185,187,189,201,203,205,209,215,217]
[[63,64,65],[323,324,325],[511,512,513],[721,722,723],[899,900,901],[1443,1444,1445],[2303,2304,2305],[2449,2450,2451],[3599,3600,3601],[3871,3872,3873],[5183,5184,5185],[5617,5618,5619],[6049,6050,6051],[6399,6400,6401],[8449,8450,8451]]
</pre>
=={{header|Modula-2}}==
<syntaxhighlight lang="modula2">MODULE DuffinianNumbers;
FROM InOut IMPORT WriteCard, WriteString, WriteLn;
CONST
MaxSigma = 10000;
VAR
seen, cur: CARDINAL;
sigma: ARRAY [1..MaxSigma] OF CARDINAL;
PROCEDURE CalculateSigmaTable;
VAR i, j: CARDINAL;
BEGIN
FOR i := 1 TO MaxSigma DO
sigma[i] := 0
END;
FOR i := 1 TO MaxSigma DO
j := i;
WHILE j <= MaxSigma DO
INC(sigma[j], i);
INC(j, i);
END
END
END CalculateSigmaTable;
PROCEDURE GCD(a, b: CARDINAL): CARDINAL;
VAR c: CARDINAL;
BEGIN
WHILE b # 0 DO
c := a MOD b;
a := b;
b := c
END;
RETURN a
END GCD;
PROCEDURE IsDuffinian(n: CARDINAL): BOOLEAN;
BEGIN
RETURN (sigma[n] > n+1) AND (GCD(n, sigma[n]) = 1)
END IsDuffinian;
PROCEDURE IsDuffinianTriple(n: CARDINAL): BOOLEAN;
BEGIN
RETURN IsDuffinian(n) AND IsDuffinian(n+1) AND IsDuffinian(n+2)
END IsDuffinianTriple;
BEGIN
CalculateSigmaTable;
WriteString("First 50 Duffinian numbers:");
WriteLn;
cur := 0;
FOR seen := 1 TO 50 DO
REPEAT INC(cur) UNTIL IsDuffinian(cur);
WriteCard(cur, 4);
IF seen MOD 10 = 0 THEN WriteLn END
END;
WriteLn;
WriteString("First 15 Duffinian triples:");
WriteLn;
cur := 0;
FOR seen := 1 TO 15 DO
REPEAT INC(cur) UNTIL IsDuffinianTriple(cur);
WriteCard(cur, 6);
WriteCard(cur+1, 6);
WriteCard(cur+2, 6);
WriteLn
END
END DuffinianNumbers.</syntaxhighlight>
{{out}}
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 15 Duffinian triples:
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451</pre>
=={{header|Nim}}==
{{trans|ALGOL 68}}
<syntaxhighlight lang="Nim">import std/[algorithm, math, strformat]
const MaxNumber = 500_000
# Construct a table of the divisor counts.
var ds: array[1..MaxNumber, int]
ds.fill 1
for i in 2..MaxNumber:
for j in countup(i, MaxNumber, i):
ds[j] += i
# Set the divisor counts of non-Duffinian numbers to 0.
ds[1] = 0 # 1 is not Duffinian.
for n in 2..MaxNumber:
let nds = ds[n]
if nds == n + 1 or gcd(n, nds) != 1:
# "n" is prime or is not relatively prime to its divisor sum.
ds[n] = 0
# Show the first 50 Duffinian numbers.
echo "First 50 Duffinian numbers:"
var dcount = 0
var n = 1
while dcount < 50:
if ds[n] != 0:
stdout.write &" {n:3}"
inc dcount
if dcount mod 25 == 0:
echo()
inc n
echo()
# Show the Duffinian triplets below MaxNumber.
echo &"The Duffinian triplets up to {MaxNumber}:"
dcount = 0
for n in 3..MaxNumber:
if ds[n - 2] != 0 and ds[n - 1] != 0 and ds[n] != 0:
inc dcount
stdout.write &" {(n - 2, n - 1, n): ^24}"
stdout.write if dcount mod 4 == 0: '\n' else: ' '
echo()
</syntaxhighlight>
{{out}}
The output is identical to that of the Algol 68 program, but the formatting is different.
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77 81 85 93 98 100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217
The Duffinian triplets up to 500000:
(63, 64, 65) (323, 324, 325) (511, 512, 513) (721, 722, 723)
(899, 900, 901) (1443, 1444, 1445) (2303, 2304, 2305) (2449, 2450, 2451)
(3599, 3600, 3601) (3871, 3872, 3873) (5183, 5184, 5185) (5617, 5618, 5619)
(6049, 6050, 6051) (6399, 6400, 6401) (8449, 8450, 8451) (10081, 10082, 10083)
(10403, 10404, 10405) (11663, 11664, 11665) (12481, 12482, 12483) (13447, 13448, 13449)
(13777, 13778, 13779) (15841, 15842, 15843) (17423, 17424, 17425) (19043, 19044, 19045)
(26911, 26912, 26913) (30275, 30276, 30277) (36863, 36864, 36865) (42631, 42632, 42633)
(46655, 46656, 46657) (47523, 47524, 47525) (53137, 53138, 53139) (58563, 58564, 58565)
(72961, 72962, 72963) (76175, 76176, 76177) (79523, 79524, 79525) (84099, 84100, 84101)
(86527, 86528, 86529) (94177, 94178, 94179) (108899, 108900, 108901) (121103, 121104, 121105)
(125315, 125316, 125317) (128017, 128018, 128019) (129599, 129600, 129601) (137287, 137288, 137289)
(144399, 144400, 144401) (144721, 144722, 144723) (154567, 154568, 154569) (158403, 158404, 158405)
(166463, 166464, 166465) (167041, 167042, 167043) (175231, 175232, 175233) (177607, 177608, 177609)
(181475, 181476, 181477) (186623, 186624, 186625) (188497, 188498, 188499) (197191, 197192, 197193)
(199711, 199712, 199713) (202499, 202500, 202501) (211249, 211250, 211251) (230399, 230400, 230401)
(231199, 231200, 231201) (232561, 232562, 232563) (236195, 236196, 236197) (242063, 242064, 242065)
(243601, 243602, 243603) (248003, 248004, 248005) (260099, 260100, 260101) (260641, 260642, 260643)
(272483, 272484, 272485) (274575, 274576, 274577) (285155, 285156, 285157) (291599, 291600, 291601)
(293763, 293764, 293765) (300303, 300304, 300305) (301087, 301088, 301089) (318095, 318096, 318097)
(344449, 344450, 344451) (354481, 354482, 354483) (359551, 359552, 359553) (359999, 360000, 360001)
(367235, 367236, 367237) (374543, 374544, 374545) (403201, 403202, 403203) (406801, 406802, 406803)
(417697, 417698, 417699) (419903, 419904, 419905) (423199, 423200, 423201) (435599, 435600, 435601)
(468511, 468512, 468513) (470449, 470450, 470451) (488071, 488072, 488073)
</pre>
=={{header|PARI/GP}}==
{{trans|Julia}}
<syntaxhighlight lang="PARI/GP">
isDuffinian(n) = (!isprime(n)) && (gcd(n, sigma(n)) == 1);
testDuffinians()=
{
print("First 50 Duffinian numbers:");
count = 0; n = 2;
while(count < 50,
if (isDuffinian(n),
print1(n, " ");
count++;
);
n++;
);
print("\n\nFifteen Duffinian triplets:");
count = 0; n = 2;
while (count < 15,
if (isDuffinian(n) && isDuffinian(n + 1) && isDuffinian(n + 2),
print(n, " ", n + 1, " ", n + 2);
count++;
);
n++;
);
}
testDuffinians();
</syntaxhighlight>
{{out}}
<pre>
First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77 81 85 93 98 100 111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217
Fifteen Duffinian triplets:
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
Line 892 ⟶ 1,915:
[166463,166464,166465] [167041,167042,167043]
</pre>
=={{header|PL/I}}==
<syntaxhighlight lang="pli">duffinianNumbers: procedure options(main);
%replace MAXSIGMA by 10000;
declare sigma (1:MAXSIGMA) fixed;
calculateSigmaTable: procedure;
declare (i, j) fixed;
do i=1 to MAXSIGMA;
sigma(i) = 0;
end;
do i=1 to MAXSIGMA;
do j=i to MAXSIGMA by i;
sigma(j) = sigma(j) + i;
end;
end;
end calculateSigmaTable;
gcd: procedure(aa,bb) returns(fixed);
declare (a, aa, b, bb, c) fixed;
a = aa;
b = bb;
do while(b > 0);
c = mod(a,b);
a = b;
b = c;
end;
return(a);
end gcd;
duffinian: procedure(n) returns(bit);
declare n fixed;
return(sigma(n) > n+1 & gcd(n, sigma(n)) = 1);
end duffinian;
triplet: procedure(n) returns(bit);
declare n fixed;
return(duffinian(n) & duffinian(n+1) & duffinian(n+2));
end triplet;
declare (i, n) fixed;
call calculateSigmaTable;
put skip list('First 50 Duffinian numbers:');
put skip;
n=0;
do i=1 to 50;
do n=n+1 repeat(n+1) while(^duffinian(n)); end;
put edit(n) (F(5));
if mod(i,10) = 0 then put skip;
end;
put skip;
put skip list('First 15 Duffinian triplets:');
n=0;
do i=1 to 15;
do n=n+1 repeat(n+1) while(^triplet(n)); end;
put skip edit(n, n+1, n+2) (F(7),F(7),F(7));
end;
end duffinianNumbers;</syntaxhighlight>
{{out}}
<pre>First 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 15 Duffinian triplets:
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451</pre>
=={{header|PL/M}}==
<syntaxhighlight lang="plm">100H:
BDOS: PROCEDURE (F,A); DECLARE F BYTE, A ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; GO TO 0; END EXIT;
PR$CHAR: PROCEDURE (C); DECLARE C BYTE; CALL BDOS(2,C); END PR$CHAR;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;
PR$NUM: PROCEDURE (N, WIDTH);
DECLARE N ADDRESS, WIDTH BYTE;
DECLARE S (6) BYTE INITIAL ('.....$');
DECLARE P ADDRESS, DG BASED P BYTE;
P = .S(5);
DIGIT:
P = P - 1;
DG = '0' + N MOD 10;
IF WIDTH > 0 THEN WIDTH = WIDTH - 1;
IF (N := N / 10) > 0 THEN GO TO DIGIT;
CALL PRINT(P);
DO WHILE WIDTH > 0;
CALL PR$CHAR(' ');
WIDTH = WIDTH - 1;
END;
END PR$NUM;
DECLARE MAX$SIGMA LITERALLY '10$001';
DECLARE SIGMA (MAX$SIGMA) ADDRESS;
CALC$SIGMA: PROCEDURE;
DECLARE (I, J) ADDRESS;
DO I = 1 TO MAX$SIGMA-1;
SIGMA(I) = 0;
END;
DO I = 1 TO MAX$SIGMA-1;
DO J = I TO MAX$SIGMA-1 BY I;
SIGMA(J) = SIGMA(J) + I;
END;
END;
END CALC$SIGMA;
GCD: PROCEDURE (X, Y) ADDRESS;
DECLARE (X, Y, Z) ADDRESS;
DO WHILE Y > 0;
Z = X MOD Y;
X = Y;
Y = Z;
END;
RETURN X;
END GCD;
DUFF: PROCEDURE (N) BYTE;
DECLARE N ADDRESS;
RETURN SIGMA(N) > N+1 AND GCD(N, SIGMA(N)) = 1;
END DUFF;
DUFF$TRIPLE: PROCEDURE (N) BYTE;
DECLARE N ADDRESS;
RETURN DUFF(N) AND DUFF(N+1) AND DUFF(N+2);
END DUFF$TRIPLE;
DECLARE N ADDRESS, I BYTE;
CALL CALC$SIGMA;
CALL PRINT(.('FIRST 50 DUFFINIAN NUMBERS:',13,10,'$'));
N = 0;
DO I = 1 TO 50;
DO WHILE NOT DUFF(N := N+1); END;
CALL PR$NUM(N, 4);
IF I MOD 10 = 0 THEN CALL PRINT(.(13,10,'$'));
END;
CALL PRINT(.(13,10,'FIRST 15 DUFFINIAN TRIPLES:',13,10,'$'));
N = 0;
DO I = 1 TO 15;
DO WHILE NOT DUFF$TRIPLE(N := N+1); END;
CALL PR$NUM(N, 6);
CALL PR$NUM(N+1, 6);
CALL PR$NUM(N+2, 6);
CALL PRINT(.(13,10,'$'));
END;
CALL EXIT;
EOF</syntaxhighlight>
{{out}}
<pre>FIRST 50 DUFFINIAN NUMBERS:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
FIRST 15 DUFFINIAN TRIPLES:
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
# duffinian.py by xing216
def factors(n):
factors = []
for i in range(1, n + 1):
if n % i == 0:
factors.append(i)
return factors
def gcd(a, b):
while b != 0:
a, b = b, a % b
return a
is_relively_prime = lambda a, b: gcd(a, b) == 1
sigma_sum = lambda x: sum(factors(x))
is_duffinian = lambda x: is_relively_prime(x, sigma_sum(x)) and len(factors(x)) > 2
count = 0
i = 0
while count < 50:
if is_duffinian(i):
print(i, end=' ')
count += 1
i+=1
count2 = 0
j = 0
while count2 < 20:
if is_duffinian(j) and is_duffinian(j+1) and is_duffinian(j+2):
print(f"({j},{j+1},{j+2})", end=' ')
count2 += 1
j+=3
j+=1
</syntaxhighlight>
=={{header|Quackery}}==
Line 1,001 ⟶ 2,248:
|
≪
DUP <span style="color:blue">∑DIV</span>
'''IF''' DUP2 1 - == '''THEN''' DROP2 0 '''ELSE''' <span style="color:blue">GCD</span> 1 == '''END'''
≫ ‘
≪ { } 2
'''WHILE''' OVER SIZE 50 < '''REPEAT'''
'''IF''' DUP '''<span style="color:blue">DUFF?</span> THEN''' SWAP OVER + SWAP '''END'''
1 +
'''END''' DROP
≫ ‘
≪ { } 4 → duff n
≪ 0 0 0
'''WHILE''' duff SIZE 15 ≤ '''REPEAT'''
ROT DROP n
'''IF''' 3 DUPN + + 3 == '''THEN'''
n 2 - n 1 - n 3 →ARRY
Line 1,021 ⟶ 2,268:
n 1 + 'n' STO '''END'''
3 DROPN duff
≫ ≫ ‘
|
get σ
if composite then check gcd(n,σ)
loop from n=2 until 50 items in list
if n is Duffinian then append to list
Line 1,035 ⟶ 2,282:
put 3 'false' boolean values in stack
loop from n=4 until 15 items in list
Line 1,052 ⟶ 2,299:
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require "prime"
class Integer
def proper_divisors(prim_div = prime_division)
return [] if self == 1
primes = prim_div.flat_map{|prime, freq| [prime] * freq}
(1...primes.size).each_with_object([1]) do |n, res|
primes.combination(n).map{|combi| res << combi.inject(:*)}
end.flatten.uniq
end
def duffinian?
pd = prime_division
return false if pd.sum(&:last) < 2
gcd(proper_divisors(pd).sum + self) == 1
end
end
n = 50
puts "The first #{n} Duffinian numbers:"
(1..).lazy.select(&:duffinian?).first(n).each_slice(10) do |slice|
puts "%4d" * slice.size % slice
end
puts "\nThe first #{n} Duffinian triplets:"
(1..).each_cons(3).lazy.select{|slice| slice.all?(&:duffinian?)}.first(n).each do |group|
puts "%8d" * group.size % group
end
</syntaxhighlight>
{{out}}
<pre>The first 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
The first 50 Duffinian triplets:
63 64 65
323 324 325
511 512 513
721 722 723
899 900 901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451
10081 10082 10083
10403 10404 10405
11663 11664 11665
12481 12482 12483
13447 13448 13449
13777 13778 13779
15841 15842 15843
17423 17424 17425
19043 19044 19045
26911 26912 26913
30275 30276 30277
36863 36864 36865
42631 42632 42633
46655 46656 46657
47523 47524 47525
53137 53138 53139
58563 58564 58565
72961 72962 72963
76175 76176 76177
79523 79524 79525
84099 84100 84101
86527 86528 86529
94177 94178 94179
108899 108900 108901
121103 121104 121105
125315 125316 125317
128017 128018 128019
129599 129600 129601
137287 137288 137289
144399 144400 144401
144721 144722 144723
154567 154568 154569
158403 158404 158405
166463 166464 166465
167041 167042 167043
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func is_duffinian(n) {
Line 1,087 ⟶ 2,426:
(8449, 8450, 8451)
</pre>
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
| |||