Here is a simple version of the code. It just enumerates the divisors and binary-searches them: 
#! /usr/bin/perl
use strict;
use Math::Pari qw(:int factorint sqrtint divisors);
for (@ARGV) {
  my $N = $_;
  my $a = factorint($N);
  my $sqrt = sqrtint($N);
  my $div = divisors($a);
  my $len = Math::Pari::matsize($div)->[1];
 
  my $low = 0;
  my $high = $len - 1;
  my $mid;
  while (1) {
     $mid = ($low + $high) >> 1;
     last unless $low < $high;
     if ($div->[$mid] > $sqrt) {
        $high = $mid - 1;
     } else {
        last if $low == $mid;
        $low = $mid;
     }
  }
  print "Result for $N is ",$div->[$mid],"\n";
}

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In reply to Re^10: OT: Finding Factor Closest To Square Root by tall_man
in thread OT: Finding Factor Closest To Square Root by QM

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