# Product of divisors

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Product of divisors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given a positive integer, return the product of its positive divisors.

Show the result for the first 50 positive integers.

## 11l

Translation of: Python
```F product_of_divisors(n)
V ans = 1
V i = 1
V j = 1
L i * i <= n
I 0 == n % i
ans *= i
j = n I/ i
I j != i
ans *= j
i++
R ans

print((1..50).map(n -> product_of_divisors(n)))```
Output:
```[1, 2, 3, 8, 5, 36, 7, 64, 27, 100, 11, 1728, 13, 196, 225, 1024, 17, 5832, 19, 8000, 441, 484, 23, 331776, 125, 676, 729, 21952, 29, 810000, 31, 32768, 1089, 1156, 1225, 10077696, 37, 1444, 1521, 2560000, 41, 3111696, 43, 85184, 91125, 2116, 47, 254803968, 343, 125000]
```

## Action!

```INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit

PROC ProdOfDivisors(INT n REAL POINTER prod)
INT i,j
REAL r

IntToReal(1,prod)
i=0
WHILE i*i<=n
DO
IF n MOD i=0 THEN
IntToReal(i,r)
RealMult(prod,r,prod)
j=n/i
IF j#i THEN
IntToReal(j,r)
RealMult(prod,r,prod)
FI
FI
i==+1
OD
RETURN

PROC Main()
BYTE i
REAL prod

Put(125) PutE() ;clear the screen
FOR i=1 TO 50
DO
ProdOfDivisors(i,prod)
PrintR(prod) Put(32)
OD
RETURN```
Output:
```1 2 3 8 5 36 7 64 27 100 11 1728 13 196 225 1024 17 5832 19 8000 441 484 23
331776 125 676 729 21952 29 810000 31 32768 1089 1156 1225 10077696 37 1444
1521 2560000 41 3111696 43 85184 91125 2116 47 254803968 343 125000
```

## ALGOL 68

Translation of: Fortran
```BEGIN # product of divisors - transaltion of the Fortran sample #
[ 1 : 50 ]INT divis;
FOR i TO UPB divis DO divis[ i ] := 1 OD;
FOR i TO UPB divis DO
FOR j FROM i BY i TO UPB divis DO
divis[ j ] *:= i
OD
OD;
FOR i TO UPB divis DO
print( ( whole( divis[ i ], -10 ) ) );
IF i MOD 5 = 0 THEN print( ( newline ) ) FI
OD
END```
Output:
```         1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000
```
Translation of: C++
```BEGIN # find the product of the divisors of the first 100 positive integers #
# calculates the number of divisors of v                                #
PROC divisor count = ( INT v )INT:
BEGIN
INT total := 1, n := v;
# Deal with powers of 2 first #
WHILE NOT ODD n DO
total +:= 1;
n  OVERAB 2
OD;
# Odd prime factors up to the square root #
INT p := 3;
WHILE ( p * p ) <= n DO
INT count := 1;
WHILE n MOD p = 0 DO
count +:= 1;
n  OVERAB p
OD;
p +:= 2;
total *:= count
OD;
# If n > 1 then it's prime #
IF n > 1 THEN total *:= 2 FI;
total
END # divisor count #;
# calculates the product of the divisors of v                            #
PROC divisor product = ( INT v )LONG INT:
BEGIN
INT      count    = divisor count( v );
LONG INT product := v ^ ( count OVER 2 );
IF ODD count THEN product *:= ENTIER sqrt( v ) FI;
product
END # divisor product # ;
BEGIN
INT limit = 50;
print( ( "Product of divisors for the first ", whole( limit, 0 ), " positive integers:", newline ) );
FOR n TO limit DO
print( ( whole( divisor product( n ), -10 ) ) );
IF n MOD 5 = 0 THEN print( ( newline ) ) FI
OD
END
END```
Output:
```Product of divisors for the first 50 positive integers:
1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000
```

## ALGOL W

Translation of: Fortran
```begin % product of divisors - transaltion of the Fortran sample %
integer array divis ( 1 :: 50 );
for i := 1 until 50 do divis( i ) := 1;
for i := 1 until 50 do begin
for j := i step i until 50 do divis( j ) := divis( j ) * i
end for_i;
for i := 1 until 50 do begin
writeon( i_w := 10, s_w := 0, divis( i ) );
if i rem 5 = 0 then write()
end for_i
end.```
Output:
```         1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000
```
Translation of: C++
```begin % find the product of the divisors of the first 100 positive integers %
% calculates the number of divisors of v                                %
integer procedure divisor_count( integer value v ) ; begin
integer total, n, p;
total := 1; n := v;
% Deal with powers of 2 first %
while not odd( n ) do begin
total := total + 1;
n     := n div 2
end while_not_odd_n ;
% Odd prime factors up to the square root %
p := 3;
while ( p * p ) <= n do begin
integer count;
count := 1;
while n rem p = 0 do begin
count := count + 1;
n     := n div p
end while_n_rem_p_eq_0 ;
p     := p + 2;
total := total * count
end while_p_x_p_le_n ;
% If n > 1 then it's prime %
if n > 1 then total := total * 2;
total
end divisor_count ;
% calculates the product of the divisors of v                            %
integer procedure divisor_product( integer value v ) ; begin
integer count, product;
count := divisor_count( v );
product := 1;
for i := 1 until count div 2 do product := product * v;
if odd( count ) then product := product * entier( sqrt( v ) );
product
end divisor_product ;
begin
integer limit;
limit := 50;
write( i_w := 1, s_w := 0, "Product of divisors for the first ", limit, " positive integers:" );
for n := 1 until limit do begin
if n rem 5 = 1 then write();
writeon( i_w := 10, s_w := 1, divisor_product( n ) )
end for_n
end
end.```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000
```

## APL

```divprod ← ×/(⍸0=⍳|⊢)
10 5 ⍴ divprod¨ ⍳50
```
Output:
```       1       2         3      8       5
36       7        64     27     100
11    1728        13    196     225
1024      17      5832     19    8000
441     484        23 331776     125
676     729     21952     29  810000
31   32768      1089   1156    1225
10077696      37      1444   1521 2560000
41 3111696        43  85184   91125
2116      47 254803968    343  125000```

## Arturo

```loop split.every:5 to [:string] map 1..50 => [product factors &] 'line [
print map line 'i -> pad i 10
]
```
Output:
```         1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

## AWK

```# syntax: GAWK -f PRODUCT_OF_DIVISORS.AWK
# converted from Go
BEGIN {
limit = 50
printf("The products of positive divisors for the first %d positive integers are:\n",limit)
for (i=1; i<=limit; i++) {
printf("%12d ",product_divisors(i))
if (i % 10 == 0) {
printf("\n")
}
}
exit(0)
}
function product_divisors(n,  ans,i,j,k) {
ans = 1
i = 1
k = (n % 2 == 0) ? 1 : 2
while (i*i <= n) {
if (n % i == 0) {
ans *= i
j = n / i
if (j != i) {
ans *= j
}
}
i += k
}
return(ans)
}
```
Output:
```The products of positive divisors for the first 50 positive integers are:
1            2            3            8            5           36            7           64           27          100
11         1728           13          196          225         1024           17         5832           19         8000
441          484           23       331776          125          676          729        21952           29       810000
31        32768         1089         1156         1225     10077696           37         1444         1521      2560000
41      3111696           43        85184        91125         2116           47    254803968          343       125000
```

## BASIC

```10 N = 50
20 DIM D(N)
30 FOR I=1 TO N: D(I)=1: NEXT
40 FOR I=2 TO N
50 FOR J=I TO N STEP I
60 D(J) = D(J)*I
70 NEXT J
80 NEXT I
90 FOR I=1 TO N: PRINT D(I),: NEXT
```
Output:
``` 1             2             3             8             5
36            7             64            27            100
11            1728          13            196           225
1024          17            5832          19            8000
441           484           23            331776        125
676           729           21952         29            810000
31            32768         1089          1156          1225
1.00777E+07   37            1444          1521          2.56E+06
41            3.1117E+06    43            85184         91125
2116          47            2.54804E+08   343           125000```

### BASIC256

```for n = 1 to 50
p = n
for i = 2 to n/2
if n mod i = 0 then p *= i
next i
if (n-1 mod 5) = 0 then print
print p; chr(9);
next n
end```

### PureBasic

```OpenConsole()
For n.i = 1 To 50
p = n
For i.i = 2 To n/2
If n % i = 0 : p * i : EndIf
Next i
;If (n-1) % 5 = 0 : PrintN("")  : EndIf
Print(Str(p) + #TAB\$)
Next n
Input()
CloseConsole()
```

### QBasic

Works with: QBasic version 1.1
Works with: QuickBasic version 4.5
```FOR n = 1 TO 50
p = n
FOR i = 2 TO n / 2
IF n MOD i = 0 THEN p = p * i
NEXT i
IF (n - 1) MOD 5 = 0 THEN PRINT
PRINT USING "###########"; p;
NEXT n
END
```

### True BASIC

```FOR n = 1 TO 50
LET p = n
FOR i = 2 TO n/2
IF MOD(n, i) = 0 THEN LET p = p * i
NEXT i
IF MOD(n-1, 5) = 0 THEN PRINT
PRINT p,
NEXT n
END
```

### Yabasic

```for n = 1 to 50
p = n
for i = 2 to n/2
if mod(n, i) = 0 then p = p * i : fi
next i
if mod(n-1, 5) = 0 then print : fi
print p using "###########";
next n
end```

## BQN

`(⊢(×´⊢/˜ 0=|˜ )1+↕)¨∘‿5⥊1+↕50`
Output:
```┌─
╵        1       2         3      8       5
36       7        64     27     100
11    1728        13    196     225
1024      17      5832     19    8000
441     484        23 331776     125
676     729     21952     29  810000
31   32768      1089   1156    1225
10077696      37      1444   1521 2560000
41 3111696        43  85184   91125
2116      47 254803968    343  125000
┘```

## C

Translation of: C++
```#include <math.h>
#include <stdio.h>

// See https://en.wikipedia.org/wiki/Divisor_function
unsigned int divisor_count(unsigned int n) {
unsigned int total = 1;
unsigned int p;

// Deal with powers of 2 first
for (; (n & 1) == 0; n >>= 1) {
++total;
}
// Odd prime factors up to the square root
for (p = 3; p * p <= n; p += 2) {
unsigned int count = 1;
for (; n % p == 0; n /= p) {
++count;
}
total *= count;
}
// If n > 1 then it's prime
if (n > 1) {
total *= 2;
}
}

// See https://mathworld.wolfram.com/DivisorProduct.html
unsigned int divisor_product(unsigned int n) {
return pow(n, divisor_count(n) / 2.0);
}

int main() {
const unsigned int limit = 50;
unsigned int n;

printf("Product of divisors for the first %d positive integers:\n", limit);
for (n = 1; n <= limit; ++n) {
printf("%11d", divisor_product(n));
if (n % 5 == 0) {
printf("\n");
}
}

return 0;
}
```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

## C++

```#include <cmath>
#include <iomanip>
#include <iostream>

// See https://en.wikipedia.org/wiki/Divisor_function
unsigned int divisor_count(unsigned int n) {
unsigned int total = 1;
// Deal with powers of 2 first
for (; (n & 1) == 0; n >>= 1)
++total;
// Odd prime factors up to the square root
for (unsigned int p = 3; p * p <= n; p += 2) {
unsigned int count = 1;
for (; n % p == 0; n /= p)
++count;
total *= count;
}
// If n > 1 then it's prime
if (n > 1)
total *= 2;
}

// See https://mathworld.wolfram.com/DivisorProduct.html
unsigned int divisor_product(unsigned int n) {
return static_cast<unsigned int>(std::pow(n, divisor_count(n)/2.0));
}

int main() {
const unsigned int limit = 50;
std::cout << "Product of divisors for the first " << limit << " positive integers:\n";
for (unsigned int n = 1; n <= limit; ++n) {
std::cout << std::setw(11) << divisor_product(n);
if (n % 5 == 0)
std::cout << '\n';
}
}
```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000
```

## Common Lisp

```(format t "~{~a ~}~%"
(loop for a from 1 to 100 collect
(loop with z = 1 for b from 1 to a
when (zerop (rem a b)) do (setf z (* z b))
finally (return z))))
```
Output:
`1 2 3 8 5 36 7 64 27 100 11 1728 13 196 225 1024 17 5832 19 8000 441 484 23 331776 125 676 729 21952 29 810000 31 32768 1089 1156 1225 10077696 37 1444 1521 2560000 41 3111696 43 85184 91125 2116 47 254803968 343 125000 2601 140608 53 8503056 3025 9834496 3249 3364 59 46656000000 61 3844 250047 2097152 4225 18974736 67 314432 4761 24010000 71 139314069504 73 5476 421875 438976 5929 37015056 79 3276800000 59049 6724 83 351298031616 7225 7396 7569 59969536 89 531441000000 8281 778688 8649 8836 9025 782757789696 97 941192 970299 1000000000 `

## COBOL

```       IDENTIFICATION DIVISION.
PROGRAM-ID.  PRODUCT-OF-DIVISORS.

DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES.
03 DIVISOR-PRODUCTS    PIC 9(9) OCCURS 50 TIMES.
03 NUM                 PIC 999.
03 MUL                 PIC 999.

01 OUTPUT-FORMAT.
03 NUM-OUT             PIC Z(9)9.
03 LINE-PTR            PIC 99 VALUE 1.
03 OUT-LINE            PIC X(50) VALUE SPACES.

PROCEDURE DIVISION.
BEGIN.
PERFORM INIT VARYING NUM FROM 1 BY 1
UNTIL NUM IS GREATER THAN 50.
PERFORM CALCULATE-MULTIPLES VARYING MUL FROM 1 BY 1
UNTIL MUL IS GREATER THAN 50.
PERFORM OUTPUT-NUM VARYING NUM FROM 1 BY 1
UNTIL NUM IS GREATER THAN 50.
STOP RUN.

INIT.
MOVE 1 TO DIVISOR-PRODUCTS(NUM).

CALCULATE-MULTIPLES.
PERFORM MULTIPLY-NUM VARYING NUM FROM MUL BY MUL
UNTIL NUM IS GREATER THAN 50.

MULTIPLY-NUM.
MULTIPLY MUL BY DIVISOR-PRODUCTS(NUM).

OUTPUT-NUM.
MOVE DIVISOR-PRODUCTS(NUM) TO NUM-OUT.
STRING NUM-OUT DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.
IF LINE-PTR IS EQUAL TO 51,
DISPLAY OUT-LINE,
MOVE SPACES TO OUT-LINE,
MOVE 1 TO LINE-PTR.
```
Output:
```         1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000```

## Cowgol

```include "cowgol.coh";

sub divprod(n: uint32): (prod: uint32) is
prod := 1;
var d := n;
while d > 1 loop
if n % d == 0 then
prod := prod * d;
end if;
d := d - 1;
end loop;
end sub;

var n: uint32 := 1;
while n <= 50 loop
var dp := divprod(n);
print_i32(dp);
print_char('\t');
if dp < 10000000 then
print_char('\t');
end if;
if n % 5 == 0 then
print_nl();
end if;
n := n + 1;
end loop;```
Output:
```1               2               3               8               5
36              7               64              27              100
11              1728            13              196             225
1024            17              5832            19              8000
441             484             23              331776          125
676             729             21952           29              810000
31              32768           1089            1156            1225
10077696        37              1444            1521            2560000
41              3111696         43              85184           91125
2116            47              254803968       343             125000```

## D

Translation of: C++
```import std.math;
import std.stdio;

// See https://en.wikipedia.org/wiki/Divisor_function
uint divisorCount(uint n) {
uint total = 1;
// Deal with powers of 2 first
for (; (n & 1) == 0; n >>= 1) {
total++;
}
// Odd prime factors up to the square root
for (uint p = 3; p * p <= n; p += 2) {
uint count = 1;
for (; n % p == 0; n /= p) {
count++;
}
total *= count;
}
// If n > 1 then it's prime
if (n > 1) {
total *= 2;
}
}

uint divisorProduct(uint n) {
return cast(uint) pow(n, divisorCount(n) / 2.0);
}

void main() {
immutable limit = 50;
writeln("Product of divisors for the first ", limit, "positive integers:");
for (uint n = 1; n <= limit; n++) {
writef("%11d", divisorProduct(n));
if (n % 5 == 0) {
writeln;
}
}
}
```
Output:
```Product of divisors for the first 50positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        124
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

## Factor

Works with: Factor version 0.99 2020-08-14
```USING: grouping io math.primes.factors math.ranges prettyprint
sequences ;

"Product of divisors for the first 50 positive integers:" print
50 [1,b] [ divisors product ] map 5 group simple-table.
```
Output:
```Product of divisors for the first 50 positive integers:
1        2       3         8      5
36       7       64        27     100
11       1728    13        196    225
1024     17      5832      19     8000
441      484     23        331776 125
676      729     21952     29     810000
31       32768   1089      1156   1225
10077696 37      1444      1521   2560000
41       3111696 43        85184  91125
2116     47      254803968 343    125000
```

## Fortran

```       program divprod
implicit none
integer divis(50), i, j
do 10 i=1, 50
10        divis(i) = 1
do 20 i=1, 50
do 20 j=i, 50, i
20            divis(j) = divis(j)*i
do 30 i=1, 50
30        if (i/5 .ne. (i-1)/5) write (*,*)
end program
```
Output:
```         1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000```

## FreeBASIC

```dim p as ulongint
for n as uinteger = 1 to 50
p = n
for i as uinteger = 2 to n/2
if n mod i = 0 then p *= i
next i
print p,
next n
```
Output:
```1             2             3             8             5             36
7             64            27            100           11            1728
13            196           225           1024          17            5832
19            8000          441           484           23            331776
125           676           729           21952         29            810000
31            32768         1089          1156          1225          10077696
37            1444          1521          2560000       41            3111696
43            85184         91125         2116          47            254803968```

## Go

```package main

import "fmt"

func prodDivisors(n int) int {
prod := 1
i := 1
k := 2
if n%2 == 0 {
k = 1
}
for i*i <= n {
if n%i == 0 {
prod *= i
j := n / i
if j != i {
prod *= j
}
}
i += k
}
return prod
}

func main() {
fmt.Println("The products of positive divisors for the first 50 positive integers are:")
for i := 1; i <= 50; i++ {
fmt.Printf("%9d  ", prodDivisors(i))
if i%5 == 0 {
fmt.Println()
}
}
}
```
Output:
```The products of positive divisors for the first 50 positive integers are:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000
```

## GW-BASIC

```10 FOR N = 1 TO 50
20 P# = N
30 FOR I = 2 TO INT(N/2)
40 IF N MOD I = 0 THEN P# = P# * I
50 NEXT I
60 PRINT P#,
70 NEXT N
```
Output:
``` 1             2             3             8             5             36            7             64            27            100           11
1728          13            196           225           1024          17            5832          19                8000          441           484
23            331776        125           676           729           21952         29            810000        31            32768         1089
1156          1225          10077696      37                1444          1521          2560000       41            3111696       43            85184
91125         2116          47            254803968     343           125000```

```import Data.List.Split (chunksOf)

------------------------- DIVISORS -----------------------

divisors :: Integral a => a -> [a]
divisors n =
((<>) <*> (rest . reverse . fmap (quot n))) \$
filter ((0 ==) . rem n) [1 .. root]
where
root = (floor . sqrt . fromIntegral) n
rest
| n == root * root = tail
| otherwise = id

-------------- SUMS AND PRODUCTS OF DIVISORS -------------

main :: IO ()
main =
mapM_
putStrLn
[ "Sums of divisors of [1..100]:",
test sum,
"Products of divisors of [1..100]:",
test product
]

test :: (Show a, Integral a) => ([a] -> a) -> String
test f =
let xs = show . f . divisors <\$> [1 .. 100]
w = maximum \$ length <\$> xs
in unlines \$
unwords
<\$> fmap
(fmap (justifyRight w ' '))
(chunksOf 5 xs)

justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)
```
Output:
```Sums of divisors of [1..100]:
1   3   4   7   6
12   8  15  13  18
12  28  14  24  24
31  18  39  20  42
32  36  24  60  31
42  40  56  30  72
32  63  48  54  48
91  38  60  56  90
42  96  44  84  78
72  48 124  57  93
72  98  54 120  72
120  80  90  60 168
62  96 104 127  84
144  68 126  96 144
72 195  74 114 124
140  96 168  80 186
121 126  84 224 108
132 120 180  90 234
112 168 128 144 120
252  98 171 156 217

Products of divisors of [1..100]:
1            2            3            8            5
36            7           64           27          100
11         1728           13          196          225
1024           17         5832           19         8000
441          484           23       331776          125
676          729        21952           29       810000
31        32768         1089         1156         1225
10077696           37         1444         1521      2560000
41      3111696           43        85184        91125
2116           47    254803968          343       125000
2601       140608           53      8503056         3025
9834496         3249         3364           59  46656000000
61         3844       250047      2097152         4225
18974736           67       314432         4761     24010000
71 139314069504           73         5476       421875
438976         5929     37015056           79   3276800000
59049         6724           83 351298031616         7225
7396         7569     59969536           89 531441000000
8281       778688         8649         8836         9025
782757789696           97       941192       970299   1000000000```

## J

```   {{ */ */@>,{ (^ i.@>:)&.>/ __ q: y }}@>:i.5 10x
1       2    3      8     5       36   7        64   27     100
11    1728   13    196   225     1024  17      5832   19    8000
441     484   23 331776   125      676 729     21952   29  810000
31   32768 1089   1156  1225 10077696  37      1444 1521 2560000
41 3111696   43  85184 91125     2116  47 254803968  343  125000
```

## Java

Translation of: C++
```public class ProductOfDivisors {
private static long divisorCount(long n) {
long total = 1;
// Deal with powers of 2 first
for (; (n & 1) == 0; n >>= 1) {
++total;
}
// Odd prime factors up to the square root
for (long p = 3; p * p <= n; p += 2) {
long count = 1;
for (; n % p == 0; n /= p) {
++count;
}
total *= count;
}
// If n > 1 then it's prime
if (n > 1) {
total *= 2;
}
}

private static long divisorProduct(long n) {
return (long) Math.pow(n, divisorCount(n) / 2.0);
}

public static void main(String[] args) {
final long limit = 50;
System.out.printf("Product of divisors for the first %d positive integers:%n", limit);
for (long n = 1; n <= limit; n++) {
System.out.printf("%11d", divisorProduct(n));
if (n % 5 == 0) {
System.out.println();
}
}
}
}
```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

gojq should be used if integer precision is to be guaranteed.

Since a `divisors` function is more likely to be generally useful than a "product of divisors" function, this entry implements the latter in terms of the former, without any appreciable cost because a streaming approach is used.

```# divisors as an unsorted stream
def divisors:
if . == 1 then 1
else . as \$n
| label \$out
| range(1; \$n) as \$i
| (\$i * \$i) as \$i2
| if \$i2 > \$n then break \$out
else if \$i2 == \$n
then \$i
elif (\$n % \$i) == 0
then \$i, (\$n/\$i)
else empty
end
end
end;

def product(s): reduce s as \$x (1; . * \$x);

def product_of_divisors: product(divisors);

# For pretty-printing
def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;```

Example

```"n   product of divisors",
Output:
```  n   product of divisors
1                1
2                2
3                3
4                8
5                5
6               36
7                7
8               64
9               27
10              100
11               11
12             1728
13               13
14              196
15              225
16             1024
17               17
18             5832
19               19
20             8000
21              441
22              484
23               23
24           331776
25              125
26              676
27              729
28            21952
29               29
30           810000
31               31
32            32768
33             1089
34             1156
35             1225
36         10077696
37               37
38             1444
39             1521
40          2560000
41               41
42          3111696
43               43
44            85184
45            91125
46             2116
47               47
48        254803968
49              343
50           125000
```

Example illustrating the use of gojq

`1234567890 | [., product_of_divisors]`
Output:
```[1234567890,157166308290967624614434966485493540963726721698403428784891012586974258380350906625255961242443130286157885664260857440235952354925000777353590796274952836151639520964606157865934675160485092641000000000000000000000000]
```

## Julia

```using Primes

function proddivisors(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 prod(f)
end

for i in 1:50
print(lpad(proddivisors(i), 10), i % 10 == 0 ? " \n" : "")
end
```
Output:
```         1         2         3         8         5        36         7        64        27       100
11      1728        13       196       225      1024        17      5832        19      8000
441       484        23    331776       125       676       729     21952        29    810000
31     32768      1089      1156      1225  10077696        37      1444      1521   2560000
41   3111696        43     85184     91125      2116        47 254803968       343    125000
```

One-liner version:

```proddivisors_oneliner(n) = prod(n%i==0 ? i : 1 for i in 1:n)
```

## Kotlin

Translation of: Java
```import kotlin.math.pow

private fun divisorCount(n: Long): Long {
var nn = n
var total: Long = 1
// Deal with powers of 2 first
while (nn and 1 == 0L) {
++total
nn = nn shr 1
}
// Odd prime factors up to the square root
var p: Long = 3
while (p * p <= nn) {
var count = 1L
while (nn % p == 0L) {
++count
nn /= p
}
total *= count
p += 2
}
// If n > 1 then it's prime
if (nn > 1) {
total *= 2
}
}

private fun divisorProduct(n: Long): Long {
return n.toDouble().pow(divisorCount(n) / 2.0).toLong()
}

fun main() {
val limit: Long = 50
println("Product of divisors for the first \$limit positive integers:")
for (n in 1..limit) {
print("%11d".format(divisorProduct(n)))
if (n % 5 == 0L) {
println()
}
}
}
```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

```            NORMAL MODE IS INTEGER
DIMENSION D(50)
THROUGH INIT, FOR I=1, 1, I.G.50
INIT        D(I)=1
THROUGH CALC, FOR I=1, 1, I.G.50
THROUGH CALC, FOR J=I, I, J.G.50
CALC        D(J) = D(J)*I
THROUGH SHOW, FOR I=1, 5, I.G.50
SHOW        PRINT FORMAT F5, D(I), D(I+1), D(I+2), D(I+3), D(I+4)
VECTOR VALUES F5 = \$5(I10)*\$
END OF PROGRAM```
Output:
```         1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000```

## Mathematica/Wolfram Language

```Divisors/*Apply[Times] /@ Range[50]
```
Output:
`{1, 2, 3, 8, 5, 36, 7, 64, 27, 100, 11, 1728, 13, 196, 225, 1024, 17, 5832, 19, 8000, 441, 484, 23, 331776, 125, 676, 729, 21952, 29, 810000, 31, 32768, 1089, 1156, 1225, 10077696, 37, 1444, 1521, 2560000, 41, 3111696, 43, 85184, 91125, 2116, 47, 254803968, 343, 125000}`

## Nim

```import math, strutils

func divisors(n: Positive): seq[int] =
result = @[1, n]
for i in 2..sqrt(n.toFloat).int:
if n mod i == 0:
let j = n div i
if i != j: result.add j

echo "Product of divisors for the first 50 positive numbers:"
for n in 1..50:
stdout.write (\$prod(n.divisors)).align(10), if n mod 5 == 0: '\n' else: ' '
```
Output:
```Product of divisors for the first 50 positive numbers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

## Perl

```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Product_of_divisors
use warnings;

my @products = ( 1 ) x 51;
for my \$n ( 1 .. 50 )
{
\$n % \$_ or \$products[\$n] *= \$_ for 1 .. \$n;
}
printf '' . (('%11d' x 5) . "\n") x 10, @products[1 .. 50];
```
Output:
```          1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000
```

## Phix

### imperative

```for i=1 to 50 do
printf(1,"%,12d",{product(factors(i,1))})
if remainder(i,5)=0 then puts(1,"\n") end if
end for
```
Output:
```           1           2           3           8           5
36           7          64          27         100
11       1,728          13         196         225
1,024          17       5,832          19       8,000
441         484          23     331,776         125
676         729      21,952          29     810,000
31      32,768       1,089       1,156       1,225
10,077,696          37       1,444       1,521   2,560,000
41   3,111,696          43      85,184      91,125
2,116          47 254,803,968         343     125,000
```

### functional

same output

```sequence r = apply(apply(true,factors,{tagset(50),{1}}),product)
puts(1,join_by(apply(true,sprintf,{{"%,12d"},r}),1,5,""))
```

## Pike

Translation of: Python
```int product_of_divisors(int n) {
int ans, i, j;
ans = i = j = 1;

while(i * i <= n) {
if(n%i == 0) {
ans = ans * i;
j = n / i;
if(j != i) {
ans = ans * j;
}
}
i = i+1;
}

return ans;
}

int main() {
int limit = 50;
write("Product of divisors for the first " + (string)limit + " positive integers:\n");
for(int i = 1; i < limit + 1; i++) {
write("%11d", product_of_divisors(i));
if(i%5 == 0) {
write("\n");
}
}
return 0;
}
```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000
```

## Python

### Finding divisors efficiently

```def product_of_divisors(n):
assert(isinstance(n, int) and 0 < n)
ans = i = j = 1
while i*i <= n:
if 0 == n%i:
ans *= i
j = n//i
if j != i:
ans *= j
i += 1
return ans

if __name__ == "__main__":
print([product_of_divisors(n) for n in range(1,51)])
```
Output:
`[1, 2, 3, 8, 5, 36, 7, 64, 27, 100, 11, 1728, 13, 196, 225, 1024, 17, 5832, 19, 8000, 441, 484, 23, 331776, 125, 676, 729, 21952, 29, 810000, 31, 32768, 1089, 1156, 1225, 10077696, 37, 1444, 1521, 2560000, 41, 3111696, 43, 85184, 91125, 2116, 47, 254803968, 343, 125000]`

### Choosing the right abstraction

This is really an exercise in defining a divisors function, and the only difference between the suggested Sum and Product draft tasks boils down to two trivial morphemes:

reduce(add, divisors(n), 0) vs reduce(mul, divisors(n), 1)

The goal of Rosetta code (see the landing page) is to provide contrastive insight (rather than comprehensive coverage of homework questions :-). Perhaps the scope for contrastive insight in the matter of divisors is already exhausted by the trivially different Proper divisors task.

```'''Sums and products of divisors'''

from math import floor, sqrt
from functools import reduce

# divisors :: Int -> [Int]
def divisors(n):
'''List of all divisors of n including n itself.
'''
root = floor(sqrt(n))
lows = [x for x in range(1, 1 + root) if 0 == n % x]
return lows + [n // x for x in reversed(lows)][
(1 if n == (root * root) else 0):
]

# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Product and sums of divisors for each integer in range [1..50]
'''
print('Products of divisors:')
for n in range(1, 1 + 50):
print(n, '->', reduce(mul, divisors(n), 1))

print('Sums of divisors:')
for n in range(1, 1 + 100):

# MAIN ---
if __name__ == '__main__':
main()
```

## Quackery

`factors` is defined at Factors of an integer#Quackery.

```  [ 1 swap factors witheach * ] is product-of-divisors ( n --> n )

[] []
50 times
[ i^ 1+ product-of-divisors join ]
witheach [ number\$ nested join ]
75 wrap\$```
Output:
```1 2 3 8 5 36 7 64 27 100 11 1728 13 196 225 1024 17 5832 19 8000 441 484 23
331776 125 676 729 21952 29 810000 31 32768 1089 1156 1225 10077696 37 1444
1521 2560000 41 3111696 43 85184 91125 2116 47 254803968 343 125000```

## R

This only takes one line.

```sapply(1:50, function(n) prod(c(Filter(function(x) n %% x == 0, seq_len(n %/% 2)), n)))
```

## Raku

Yet more tasks that are tiny variations of each other. Tau function, Tau number, Sum of divisors and Product of divisors all use code with minimal changes. What the heck, post 'em all.

```use Prime::Factor:ver<0.3.0+>;
use Lingua::EN::Numbers;

say "\nTau function - first 100:\n",        # ID
(1..*).map({ +.&divisors })[^100]\          # the task
.batch(20)».fmt("%3d").join("\n");          # display formatting

say "\nTau numbers - first 100:\n",         # ID
(1..*).grep({ \$_ %% +.&divisors })[^100]\   # the task
.batch(10)».&comma».fmt("%5s").join("\n");  # display formatting

say "\nDivisor sums - first 100:\n",        # ID
(1..*).map({ [+] .&divisors })[^100]\       # the task
.batch(20)».fmt("%4d").join("\n");          # display formatting

say "\nDivisor products - first 100:\n",    # ID
(1..*).map({ [×] .&divisors })[^100]\       # the task
.batch(5)».&comma».fmt("%16s").join("\n");  # display formatting
```
Output:
```Tau function - first 100:
1   2   2   3   2   4   2   4   3   4   2   6   2   4   4   5   2   6   2   6
4   4   2   8   3   4   4   6   2   8   2   6   4   4   4   9   2   4   4   8
2   8   2   6   6   4   2  10   3   6   4   6   2   8   4   8   4   4   2  12
2   4   6   7   4   8   2   6   4   8   2  12   2   4   6   6   4   8   2  10
5   4   2  12   4   4   4   8   2  12   4   6   4   4   4  12   2   6   6   9

Tau numbers - first 100:
1     2     8     9    12    18    24    36    40    56
60    72    80    84    88    96   104   108   128   132
136   152   156   180   184   204   225   228   232   240
248   252   276   288   296   328   344   348   360   372
376   384   396   424   441   444   448   450   468   472
480   488   492   504   516   536   560   564   568   584
600   612   625   632   636   640   664   672   684   708
712   720   732   776   792   804   808   824   828   852
856   864   872   876   880   882   896   904   936   948
972   996 1,016 1,040 1,044 1,048 1,056 1,068 1,089 1,096

Divisor sums - first 100:
1    3    4    7    6   12    8   15   13   18   12   28   14   24   24   31   18   39   20   42
32   36   24   60   31   42   40   56   30   72   32   63   48   54   48   91   38   60   56   90
42   96   44   84   78   72   48  124   57   93   72   98   54  120   72  120   80   90   60  168
62   96  104  127   84  144   68  126   96  144   72  195   74  114  124  140   96  168   80  186
121  126   84  224  108  132  120  180   90  234  112  168  128  144  120  252   98  171  156  217

Divisor products - first 100:
1                2                3                8                5
36                7               64               27              100
11            1,728               13              196              225
1,024               17            5,832               19            8,000
441              484               23          331,776              125
676              729           21,952               29          810,000
31           32,768            1,089            1,156            1,225
10,077,696               37            1,444            1,521        2,560,000
41        3,111,696               43           85,184           91,125
2,116               47      254,803,968              343          125,000
2,601          140,608               53        8,503,056            3,025
9,834,496            3,249            3,364               59   46,656,000,000
61            3,844          250,047        2,097,152            4,225
18,974,736               67          314,432            4,761       24,010,000
71  139,314,069,504               73            5,476          421,875
438,976            5,929       37,015,056               79    3,276,800,000
59,049            6,724               83  351,298,031,616            7,225
7,396            7,569       59,969,536               89  531,441,000,000
8,281          778,688            8,649            8,836            9,025
782,757,789,696               97          941,192          970,299    1,000,000,000```

## REXX

```/*REXX program displays the first  N  product of divisors  (shown in a columnar format).*/
numeric digits 20                                /*ensure enough decimal digit precision*/
parse arg n cols .                               /*obtain optional argument from the CL.*/
if    n=='' |    n==","  then    n= 50           /*Not specified?  Then use the default.*/
if cols=='' | cols==","  then cols=  5           /* "      "         "   "   "     "    */
say ' index │'center("product of divisors", 102)       /*display title for the column #s*/
say '───────┼'center(""                   , 102,'─')   /*   "      "   separator (above)*/
w= max(20, length(n) )                           /*W:  used to align 1st output column. */
\$=;                            idx= 1            /*\$:  the output list, shown in columns*/
do j=1  for N                             /*process  N  positive integers.       */
\$= \$  ||  right( commas( sigma(j) ), 20)  /*add a sigma (sum) to the output list.*/
if j//cols\==0  then iterate              /*Not a multiple of cols? Don't display*/
say center(idx, 7)'│'             \$       /*display partial list to the terminal.*/
idx= idx + cols                           /*bump the index number for the output.*/
end   /*j*/

if \$\==''  then say center(idx, 7)' '    \$       /*any residuals sums left to display?  */
say '───────┴'center(""                   , 102,'─')   /*   "      "   separator (above)*/
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 ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
sigma: procedure; parse arg x; if x==1 then return 1;  odd=x // 2    /* // ◄──remainder.*/
p= x                                      /* [↓]  only use  EVEN or ODD integers.*/
do k=2+odd  by 1+odd  while k*k<x   /*divide by all integers up to  √x.    */
if x//k==0  then p= p * k * (x % k) /*multiple the two divisors to product.*/
end   /*k*/                         /* [↑]  %  is the REXX integer division*/
if k*k==x  then  return p * k             /*Was  X  a square?   If so, add  √ x  */
return p                 /*return (sigma) sum of the divisors.  */
```
output   when using the default input:
``` index │                                         product of divisors
───────┼──────────────────────────────────────────────────────────────────────────────────────────────────────
1   │                    1                   2                   3                   8                   5
6   │                   36                   7                  64                  27                 100
11   │                   11               1,728                  13                 196                 225
16   │                1,024                  17               5,832                  19               8,000
21   │                  441                 484                  23             331,776                 125
26   │                  676                 729              21,952                  29             810,000
31   │                   31              32,768               1,089               1,156               1,225
36   │           10,077,696                  37               1,444               1,521           2,560,000
41   │                   41           3,111,696                  43              85,184              91,125
46   │                2,116                  47         254,803,968                 343             125,000
───────┴──────────────────────────────────────────────────────────────────────────────────────────────────────
```

## Ring

```limit = 50
row = 0

see "working..." + nl

for n = 1 to limit
pro = 1
for m = 1 to n
if n%m = 0
pro = pro*m
ok
next
see "" + pro + " "
row = row + 1
if row % 5 = 0
see nl
ok
next

see "done..." + nl```
Output:
```working...
1 2 3 8 5
36 7 64 27 100
11 1728 13 196 225
1024 17 5832 19 8000
441 484 23 331776 125
676 729 21952 29 810000
31 32768 1089 1156 1225
10077696 37 1444 1521 2560000
41 3111696 43 85184 91125
2116 47 254803968 343 125000
done...
```

## Ruby

Translation of: C++
```def divisor_count(n)
total = 1
# Deal with powers of 2 first
while n % 2 == 0 do
total = total + 1
n = n >> 1
end
# Odd prime factors up to the square root
p = 3
while p * p <= n do
count = 1
while n % p == 0 do
count = count + 1
n = n / p
end
total = total * count
p = p + 2
end
# If n > 1 then it's prime
if n > 1 then
total = total * 2
end
end

def divisor_product(n)
return (n ** (divisor_count(n) / 2.0)).floor
end

LIMIT = 50
print "Product of divisors for the first ", LIMIT, " positive integers:\n"
for n in 1 .. LIMIT
print "%11d" % [divisor_product(n)]
if n % 5 == 0 then
print "\n"
end
end
```
Output:
```Product of divisors for the first 50 positive integers:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000```

## Verilog

```module main;
integer p, n, i;

initial begin
for(n = 1; n <= 50; n=n+1)
begin
p = n;
for(i = 2; i <= n/2; i=i+1) if (n % i == 0) p = p * i;
\$display(p);
end
\$finish ;
end
endmodule
```

## VTL-2

This sample only shows the divisor products of the first 20 numbers as (the original) VTL-2 only handles numbers in the range 0-65535. The divisor product of 24 would overflow.
Note, all VTL-2 operators are single characters, however though the "<" operator does a lexx-than test, the ">" operator tests greater-than-or-equal.

```100 M=20
110 I=0
120 I=I+1
130 :I)=1
140 #=I<M*120
150 I=0
160 I=I+1
170 J=0
180 J=J+I
190 :J)=:J)*I
200 #=J<M*180
210 #=I<M*160
220 I=0
230 I=I+1
240 V=:I)
250 #=V>10*270
260 \$=32
270 #=V>100*290
280 \$=32
290 #=V>1000*310
300 \$=32
310 #=V>10000*330
320 \$=32
330 ?=:I)
340 \$=32
350 #=I/5*0+%=0=0*370
360 ?=""
370 #=I<M*230```
Output:
```    1     2     3     8     5
36     7    64    27   100
11  1728    13   196   225
1024    17  5832    19  8000
```

## Wren

Library: Wren-math
Library: Wren-fmt
```import "/math" for Int, Nums
import "/fmt" for Fmt

System.print("The products of positive divisors for the first 50 positive integers are:")
for (i in 1..50) {
Fmt.write("\$9d  ", Nums.prod(Int.divisors(i)))
if (i % 5 == 0) System.print()
}
```
Output:
```The products of positive divisors for the first 50 positive integers are:
1          2          3          8          5
36          7         64         27        100
11       1728         13        196        225
1024         17       5832         19       8000
441        484         23     331776        125
676        729      21952         29     810000
31      32768       1089       1156       1225
10077696         37       1444       1521    2560000
41    3111696         43      85184      91125
2116         47  254803968        343     125000
```

## XPL0

```func ProdDiv(N);        \Return product of divisors of N
int  N, Prod, Div;
[Prod:= 1;
for Div:= 2 to N do
if rem(N/Div) = 0 then
Prod:= Prod * Div;
return Prod;
];

int C, N;
[Format(10, 0);
C:= 0;
for N:= 1 to 50 do
[RlOut(0, float(ProdDiv(N)));
C:= C+1;
if rem(C/5) = 0 then CrLf(0)];
]```
Output:
```         1         2         3         8         5
36         7        64        27       100
11      1728        13       196       225
1024        17      5832        19      8000
441       484        23    331776       125
676       729     21952        29    810000
31     32768      1089      1156      1225
10077696        37      1444      1521   2560000
41   3111696        43     85184     91125
2116        47 254803968       343    125000
```