\begin{definition}[Definition:Liouville Function]
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.
\end{definition}