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:

 μ(1) is defined to be 1.
 μ(n) = 1 if n is a square-free positive integer with an even number of prime factors.
 μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors.
 μ(n) = 0 if n has a squared prime factor.


Task

 Write a routine (function, procedure, whatever) μ(n) to find the Möbius number for a positive integer n.
 Use that routine to find and display here, on this page, at least the first 99 terms in a grid layout. (Not just one long line or column of numbers.)


See also

 Wikipedia: Möbius function


Related Tasks

 Mertens function


use Prime::Factor;
 
sub μ (Int \n) {
    return 0 if n %% 4 or n %% 9 or n %% 25 or n %% 49 or n %% 121;
    my @p = prime-factors(n);
    +@p == +@p.unique ?? +@p %% 2 ?? 1 !! -1 !! 0
}
 
my @möbius = lazy flat '', 1, (2..*).hyper.map: -> \n { μ(n) };
 
# The Task
put "Möbius sequence - First 199 terms:\n",
    @möbius[^200]».fmt('%3s').batch(20).join: "\n";