Solution
= Solution
Let $\mathbf1(n)=1$. The basic <Von Mangoldt divisor identity> is
$$
\log n=\sum_{d\mid n}\Lambda(d),
$$
because if $n=\prod_pp^{v_p(n)}$, the right-hand side is $\sum_pv_p(n)\log p=\log n$. In terms of <Dirichlet convolution>, this says $\log=\mathbf1*\Lambda$. Since the <Möbius function> is the convolution inverse of $\mathbf1$, convolving with $\mu$ gives $\Lambda=\mu*\log$. Consequently
$$
\Lambda(n)=\sum_{d\mid n}\mu(d)\log\frac nd.
$$