Mangoldt function

The Mangoldt function $\Lambda$ is defined by

\Lambda(n)=\begin{cases}\ln p,&\text{if $n=p^{k}$, where $p$ is a prime and $k% $ is a natural number $\geq 1$}\\ 0,&\text{otherwise}\end{cases}

The Moebius Inversion Formula leads to the identity $\Lambda(n)=\sum_{d|n}\mu(n/d)\ln d=-\sum_{d|n}\mu(d)\ln d$ .