Mean Values of a Class of Arithmetical Functions

Deyu Zhang^{1}

School of Mathematical Sciences Shandong Normal University

Jinan 250014 Shandong P. R. China

zdy 78@yahoo.com.cn

Wenguang Zhai^{1} Department of Mathematics

China University of Mining and Technology Beijing, 100083 P. R. China

zhaiwg@hotmail.com

Abstract

In this paper we consider a class of functions U of arithmetical functions which include P̃(n)/n, where P̃(n) := n ∏_{p|n}(2 − \frac{1}{p}). For any given U ∈ U, we obtain the asymptotic formula for ∑_{n≤x} U(n), which improves a result of De Koninck and Kátai.

1This work is supported by National Natural Science Foundation of China(Grant Nos. 10771127, 11001154) and Shandong Province Natural Science Foundation (Nos. BS2009SF018, ZR2010AQ009).