34 lines
907 B
Perl
34 lines
907 B
Perl
use utf8;
|
|
use strict;
|
|
use warnings;
|
|
use feature 'say';
|
|
use List::Util 'uniq';
|
|
|
|
sub prime_factors {
|
|
my ($n, $d, @factors) = (shift, 1);
|
|
while ($n > 1 and $d++) {
|
|
$n /= $d, push @factors, $d until $n % $d;
|
|
}
|
|
@factors
|
|
}
|
|
|
|
sub μ {
|
|
my @p = prime_factors(shift);
|
|
@p == uniq(@p) ? 0 == @p%2 ? 1 : -1 : 0
|
|
}
|
|
|
|
sub progressive_sum {
|
|
my @sum = shift @_;
|
|
push @sum, $sum[-1] + $_ for @_;
|
|
@sum
|
|
}
|
|
|
|
my($upto, $show, @möebius) = (1000, 199, ());
|
|
push @möebius, μ($_) for 1..$upto;
|
|
my @mertens = progressive_sum @möebius;
|
|
|
|
say "Mertens sequence - First $show terms:\n" .
|
|
(' 'x4 . sprintf "@{['%4d' x $show]}", @mertens[0..$show-1]) =~ s/((.){80})/$1\n/gr .
|
|
sprintf("\nEquals zero %3d times between 1 and $upto", scalar grep { ! $_ } @mertens) .
|
|
sprintf "\nCrosses zero%3d times between 1 and $upto", scalar grep { ! $mertens[$_-1] and $mertens[$_] } 1 .. @mertens;
|