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:
:*; [[wp:Möbius function|Wikipedia: Möbius function]]


;Related Tasks:
:*; [[Mertens function]]
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