Definition:Liouville Function
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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
Source of Name
This entry was named for Joseph Liouville.