#!/usr/bin/perl -w
use strict;

my %f = ( 2 => 2, 3 => 1, 5 => 1, 11 => 1, 277412413 => 1 );
my @f = sort { $a <=> $b } keys %f;

my @d = @f;
my( %d, %x );
for my $i ( 0..$#f ) {
    my $f = $f[$i];
    ( $d{$f} = [(0)x@f] )->[$i]++;
    $x{$f} = $i;
}

for my $i ( 0..$#f ) {
    my $f = $f[$i];
    my $p = $f{$f};
    my @t = @d;
    for my $e ( 1..$f{$f} ) {
        my( @t2, @m, @n );
        while( @t ) {
            my $t = shift @t;
            merge( \@n, $t, \@m, 1 < $e ? \@d : () );
            push @n, $t
                if  1 == $e;
            if(     $d{$t}[$i] < $p
                &&  $x{$t} <= $i    # Avoid duplicates
            ) {
                my $m = $t*$f;
                push @m, $m;
                push @t2, $m;
                ( $d{$m} = [@{ $d{$t} }] )->[$i]++;
                $x{$m} = $i
                    if  ! $x{$m} || $x{$m} < $i;
            }
        }
        @t = @t2;
        merge( \@n, 0, \@m, 1 < $e ? \@d : () );
        @d = @n;
    }
}

print "Factors:";
for my $f ( @f ) {
    if( 1 < $f{$f} ) {
        print " $f^$f{$f}";
    } else {
        print " $f";
    }
}
print "\nDivisors: 1 @d\n";
exit;


sub merge {
    my( $to_av, $max, $from_av, @rest ) = @_;
    if( $max ) {
        while( @$from_av && $from_av->[0] < $max ) {
            my $next = shift @$from_av;
            merge( $to_av, $next, @rest )
                if  @rest;
            push @$to_av, $next;
        }
        merge( $to_av, $max, @rest )
            if  @rest;
    } elsif( @rest ) {
        while( @$from_av ) {
            my $next = shift @$from_av;
            merge( $to_av, $next, @rest );
            push @$to_av, $next;
        }
        merge( $to_av, 0, @rest );
    } else {
        push @$to_av, @$from_av;
        @$from_av = ();
    }
}

##</code><code>##

Factors: 2^2 3 5 11 277412413
Divisors: 1 2 3 4 5 6 10 11 12 15 20 22 30 33 44 55 60 66 110 132 165 220 330 660 277412413 554824826 832237239 1109649652 1387062065 1664474478 2774124130 3051536543 3328948956 4161186195 5548248260 6103073086 8322372390 9154609629 12206146172 15257682715 16644744780 18309219258 30515365430 36618438516 45773048145 61030730860 91546096290 183092192580