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Product of divisors

From Rosetta Code
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.

Task

Show the result for the first 50 positive integers.



11l[edit]

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]

ALGOL 68[edit]

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[edit]

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[edit]

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

AWK[edit]

 
# 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[edit]

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

C[edit]

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;
}
return total;
}
 
// 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++[edit]

#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;
return total;
}
 
// 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[edit]

 
(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 

Cowgol[edit]

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[edit]

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;
}
return total;
}
 
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[edit]

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[edit]

       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
write (*,'(I10)',advance='no') divis(i)
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[edit]

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[edit]

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[edit]

 
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

Haskell[edit]

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

Java[edit]

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;
}
return total;
}
 
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

Julia[edit]

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

Kotlin[edit]

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
}
return total
}
 
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

MAD[edit]

            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

Nim[edit]

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
result.add 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[edit]

#!/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[edit]

imperative[edit]

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[edit]

same output

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

Python[edit]

Finding divisors efficiently[edit]

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[edit]

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
from operator import add, mul
 
 
# 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):
print(n, '->', reduce(add, divisors(n), 0))
 
 
# MAIN ---
if __name__ == '__main__':
main()

Raku[edit]

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[edit]

/*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.*/
$= /*start with a blank line for next time*/
end /*j*/
 
if $\=='' then say center(idx, 7)' ' $ /*any residuals sums left to display? */
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[edit]

 
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[edit]

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
return total
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

Wren[edit]

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