# 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.

## Source of Name

This entry was named for Joseph Liouville.