Introduction to Analytic Number Theory
《Introduction to Analytic Number Theory》 · 第 46 页 · Section 2.19「The Selberg identity」，Theorem 2.27
The Selberg identity. For $n\ge1$ we have $\Lambda(n)\log n+\sum_{d\mid n}\Lambda(d)\Lambda(n/d)=\sum_{d\mid n}\mu(d)\log^2(n/d)$.