#! /usr/bin/perl use strict; use Math::Pari qw(:int factorint divisors); for (@ARGV) { my \$N = \$_; my \$a = factorint(\$N); my \$div = divisors(\$a); print "sorted list of divisors of \$N is ",\$div,"\n"; } ##```## perl ddd.pl 12345 sorted list of divisors of 12345 is [1,3,5,15,823,2469,4115,12345] ##``````## module Powerset where {- Expand muliplies of two list of numbers. For example: mult_expand [1, 2, 4] [1, 5] Produces: [[1,5],[2,10],[4,20]] -} mult_expand p [] = p:[] mult_expand p lst = map (\x -> map (*x) lst) p {- expand the powers of x from 0 to exp -} pows x exp = map (\e -> x^e) [0..exp] {- expand the powers the first item in a pair from 0 to the second item in the pair. -} powerlst p = pows (fst p) (snd p) {- One stage of a merge sort -} merge [] ys = ys merge xs [] = xs merge (x:xs) (y:ys) = if x <= y then x : merge xs (y:ys) else y : merge (x:xs) ys {- Do multiple merges to get an ordered list. -} bigmerge lsts = foldl merge [] lsts {- The complete power set of a list of factor/exponent pairs. For example: powerset [(2,3),(5,1)] Produces: [1,2,4,5,8,10,20,40] -} powerset [] = [] powerset (x:xs) = bigmerge (mult_expand (powerlst x) (powerset xs)) {- Helper function for factor_sqrt. Finds the last list value less than or equal to the given limit. -} fsqrt lim lastgood [] = lastgood fsqrt lim lastgood (x:xs) = if (x > lim) then lastgood else fsqrt lim x xs {- Find the last divisor less than the square root, given the number and its factors -} factor_sqrt n factors = fsqrt (sqrt n) 0 (powerset factors) ##``````## Prelude> :l Powerset.hs Powerset> factor_sqrt 24777695232 [(2,13),(3,8),(461,1)] 149364.0 ```