In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that is neither multiplicative nor additive. == Definition == The von Mangoldt function, denoted by Λ(n), is defined as Λ(n)={log⁡pif n=pk for some prime p and integer k≥1,0otherwise.{\displaystyle \Lambda (n)={\begin{cases}\log p&{\text{if }}n=p^{k}{\text{ for some prime }}p{\text{ and integer }}k\geq 1,\\0&{\text{otherwise.}}\end{cases}}}The values of Λ(n) for the first nine positive integers (i.e. natural numbers) are 0...