Journal of Integer Sequences, Vol. 14 (2011), Article 11.6.5

Mean Values of a Class of Arithmetical Functions


Deyu Zhang
School of Mathematical Sciences
Shandong Normal University
Jinan 250014
Shandong
P. R. China

Wenguang Zhai
Department of Mathematics
China University of Mining and Technology
Beijing, 100083
P. R. China

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.

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(Concerned with sequences A018804 A176345.)

Received January 25 2011; revised version received May 24 2011. Published in Journal of Integer Sequences, June 10 2011.

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