Abstract: For any given positive integer m≥2 and any natural number n, we call a_m(n) represents a m-th power complement number. Elementary methods is used to study the mean value properties of the series \sum\limits_n = 1^\infty \fracn\left(na_m\left(n \right) \right)^s , where s is a complex number with Res≥2, and several identities are work out.