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 $\\Lambda(n)=\\sum_{d|n}\\mu(n/d)\\ln d=-\\sum_{d|n}\\mu(d)\\ln d$ .

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