Definition:Liouville Function

Definition
Let $n \in \Z_{>0}$, that is, a strictly positive integer.

The Liouville function is the function $\lambda: \Z_{>0} \to \Z_{>0}$ defined as:
 * $\lambda \left({n}\right) = \left({-1}\right)^{\Omega \left({n}\right)}$

where $\Omega \left({n}\right)$ is the number of prime factors of $n$, counted with multiplicity.

Also see

 * Liouville Function is Multiplicative