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#!/usr/bin/env perl
use warnings;
use strict;
use Math::Prime::Util qw/:all/;
# Fill in the chains
my @achain = ( [0] );
foreach my $n (0 .. 50_000) {
next if defined $achain[$n];
my @seq = aliquot_sequence($n, 1_000_000);
#print "chain for $n = ", join(",", @seq), "\n";
while (@seq) {
my $s = shift @seq;
$achain[$s] = [$s, @seq] if !defined $achain[$s];
}
}
# Find max chain length
my ($maxlen, $maxn) = (0, 0);
foreach my $n (0 .. 1_000_000) {
next unless defined $achain[$n];
next unless $achain[$n]->[0] == $achain[$n]->[-1];
my $len = scalar @{$achain[$n]} - 1;
($maxlen, $maxn) = ($len, $n) if $len > $maxlen;
}
print "Max length: $maxlen. n = $maxn\n";
print "Chain for $maxn: ", join(",", @{$achain[$maxn]}), "\n";
sub aliquot_sequence {
my ($n, $max) = @_;
my %hash;
undef $hash{$n};
my @seq = ($n);
foreach my $len (1 .. 1000) {
$n = divisor_sum($n)-$n;
# Stop if we have exceeded the threshold
last if $n > $max;
# If we know how this chain ends, return it now
return @seq, @{$achain[$n]} if defined $achain[$n];
push @seq, $n;
return @seq if exists $hash{$n} || $n == 0;
undef $hash{$n};
}
return ();
}
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