quality:correction
Definition

For any positive integer n, define μ (n) as the sum of the primitive n th roots of unity. It has values in { − 1, 0, 1} depending on the factorization of n into prime factors:

The Möbius function can alternatively be represented as

where δ is the Kronecker delta, λ (n) is the Liouville function, ω (n) is the number of distinct prime divisors of n, and Ω(n) is the number of prime factors of n, counted with multiplicity.

It can also be defined as the Dirichlet convolution inverse of the constant function f (n) = 1 {\displaystyle f(n)=1}.