Mobius

model is sweet Amit.

μ(n) is defined for all strictly positive natural numbers n and has its values in {−1, 0, 1} depending on the factorization of n into prime factors. It is defined as follows

* μ(n) = 1 if n is a square-free positive integer with an even number of distinct prime factors.
* μ(n) = −1 if n is a square-free positive integer with an odd number of distinct prime factors.
* μ(n) = 0 if n is not square-free.

This is taken to imply that μ(1) = 1. The value of μ(0) is generally left undefined, but the Maple computer algebra system for example returns −1 for this value.

Alternatively, μ(n) = (-1)^ω(n) * [1 - sgn(Ω(n) - ω(n))] , which applies for n>=1 since ω(1)=0 and Ω(1)=0.