Data commit

Task/Mertens-function/Perl/mertens-function.pl

@@ -0,0 +1,33 @@
+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;