Summary: Two new arithmetical functions \(U(n)\) and \(V(n)\) are defined, and the convergence properties of the Dirichlet series \(\sum\limits_{n=1}^\infty\frac{(-1)^n}{U^s(n)}\) and \(\sum\limits_{n=1}^\infty\frac{(-1)^n}{V^s(n)}\) are studied. By using the elementary and analytic method, identities of Dirichlet series of these two arithmetic functions and two interesting mean value theorems are obtained.