How to resolve the algorithm Möbius function step by step in the Perl programming language

Published on 12 May 2024 09:40 PM
#Perl

How to resolve the algorithm Möbius function step by step in the Perl programming language

Table of Contents

Problem Statement

The classical Möbius function: μ(n) is an important multiplicative function in number theory and combinatorics. There are several ways to implement a Möbius function. A fairly straightforward method is to find the prime factors of a positive integer n, then define μ(n) based on the sum of the primitive factors. It has the values {−1, 0, 1} depending on the factorization of n:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Möbius function step by step in the Perl programming language

Source code in the perl programming language

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;
}

my @möebius;
push @möebius, μ($_) for 1 .. (my $upto = 199);

say "Möbius sequence - First $upto terms:\n" .
    (' 'x4 . sprintf "@{['%4d' x $upto]}", @möebius) =~ s/((.){80})/$1\n/gr;

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