Definition:Von Mangoldt Function

Definition
The von Mangoldt function $\Lambda: \N \to \R$ is defined as:


 * $\Lambda \left({n}\right) = \begin{cases}

\ln \left({p}\right) & : \exists m \in \N, p \in \mathbb P: n = p^m \\ 0 & : \text{otherwise} \end{cases}$

where $\mathbb P$ is the set of all prime numbers.

Also known as
Some sources dispose of the von, and instead refer to this as the Mangoldt function.