The Mean Value Of Arithmetic Function On Special Sequencs

In this paper,we studied the mean value and the hybrid mean value of some number theory functions.The main achievements contained in this dissertation are as follows:1.The mean value of the divisor function d(n)in square-free counts was studied by using the analytic methods,obtained a asymptotic fbrmula of this function.2.The mean value of the number theory function d₁(n) in square-full counts was studied by using the analytic methods,obtained a asymptotic fbrmula of this function.3.The mean value of several kinds of special Smarnadache function was studied by using the elementary methods and analytic methods,obtained some new asymptotic formulae.