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Mean Values of a Class of
Arithmetical Functions Deyu Zhang¹
School of Mathematical Sciences
Shandong Normal University
Jinan 250014
Shandong
P. R. China
mailto:zdy_78@yahoo.com.cnzdy_78@yahoo.com.cn

Wenguang Zhai$^1$
Department of Mathematics
China University of Mining and Technology
Beijing, 100083
P. R. China
mailto:zhaiwg@hotmail.comzhaiwg@hotmail.com

Abstract:

In this paper we consider a class of functions $\mathcal {U}$ of arithmetical functions which include $\tilde{P}(n)/n$, where $\tilde{P}(n):=n \prod_{p\vert n}(2-\frac{1}{p})$. For any given $U\in\mathcal {U}$, we obtain the asymptotic formula for $\sum_{n\leq x}U(n)$, which improves a result of De Koninck and Kátai.