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#!/usr/bin/env perl
use strict;
use warnings;
use Test::More;
use Math::Prime::Util qw/divisor_sum/;
my $extra = defined $ENV{EXTENDED_TESTING} && $ENV{EXTENDED_TESTING};
#my $usexs = Math::Prime::Util::prime_get_config->{'xs'};
#my $usegmp= Math::Prime::Util::prime_get_config->{'gmp'};
#my $use64 = Math::Prime::Util::prime_get_config->{'maxbits'} > 32;
#$use64 = 0 if $use64 && 18446744073709550592 == ~0;
my %sigmak = (
# A0000005
0 => [1,2,2,3,2,4,2,4,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,8,3,4,4,6,2,8,2,6,4,4,4,9,2,4,4,8,2,8,2,6,6,4,2,10,3,6,4,6,2,8,4,8,4,4,2,12,2,4,6,7,4,8,2,6,4,8,2,12,2,4,6,6,4,8,2,10,5,4,2,12,4,4,4,8,2,12,4,6,4,4,4,12,2,6,6,9,2,8,2,8],
# A000203
1 => [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],
# A001157
2 => [1, 5, 10, 21, 26, 50, 50, 85, 91, 130, 122, 210, 170, 250, 260, 341, 290, 455, 362, 546, 500, 610, 530, 850, 651, 850, 820, 1050, 842, 1300, 962, 1365, 1220, 1450, 1300, 1911, 1370, 1810, 1700, 2210, 1682, 2500, 1850, 2562, 2366, 2650, 2210, 3410, 2451, 3255],
# A001158
3 => [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198, 9632, 11988, 12168, 16380, 15751, 19782, 20440, 25112, 24390, 31752, 29792, 37449, 37296, 44226, 43344, 55261, 50654, 61740, 61544],
);
my @tau4 = (1,4,4,10,4,16,4,20,10,16,4,40,4,16,16,35,4,40,4,40,16,16,4,80,10,16,20,40,4,64,4,56,16,16,16,100);
push @tau4, (4,16,16,80,4,64,4,40,40,16,4,140,10,40,16,40,4,80,16,80,16,16,4,160,4,16,40,84,16,64,4,40,16,64,4,200,4,16,40,40,16) if $extra;
plan tests => 1 + 2*scalar(keys %sigmak) + 3;
###### Divisor sum
while (my($k, $sigmaref) = each (%sigmak)) {
my @slist;
foreach my $n (1 .. scalar @$sigmaref) {
push @slist, divisor_sum( $n, sub { int($_[0] ** $k) } );
}
is_deeply( \@slist, $sigmaref, "Sum of divisors to the ${k}th power: Sigma_$k" );
@slist = ();
foreach my $n (1 .. scalar @$sigmaref) {
push @slist, divisor_sum( $n, $k );
}
is_deeply( \@slist, $sigmaref, "Sigma_$k using integer instead of sub" );
}
# k=1 standard sum -- much faster
{
my @slist = map { divisor_sum($_) } 1 .. scalar @{$sigmak{1}};
is_deeply(\@slist, $sigmak{1}, "divisor_sum(n)");
}
# tau two ways
{
my $len = scalar @{$sigmak{0}};
my @slist1 = map { divisor_sum($_, sub {1}) } 1 .. $len;
my @slist2 = map { divisor_sum($_, 0 ) } 1 .. $len;
is_deeply( \@slist1, $sigmak{0}, "tau as divisor_sum(n, sub {1})" );
is_deeply( \@slist2, $sigmak{0}, "tau as divisor_sum(n, 0)" );
}
{
# tau_4 A007426
my @t;
foreach my $n (1 .. scalar @tau4) {
push @t, divisor_sum($n, sub { divisor_sum($_[0],sub { divisor_sum($_[0],0) }) });
}
is_deeply( \@t, \@tau4, "Tau4 (A007426), nested divisor sums" );
}
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