Journal of Integer Sequences, Vol. 16 (2013), Article 13.6.5

On an Open Problem of Tóth


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 a recent paper, Tóth mentioned that it is an open problem to give the asymptotic formula for $\sum_{n\leq x}P^{k}(n)$, where P(n) is the well-known gcd-sum function and $k\geq 2$ is a fixed integer. In this paper, we use the analytic properties of the Dirichlet divisor function to obtain the asymptotic formula for it.

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(Concerned with sequence A018804.)

Received January 10 2013; revised versions received March 6 2013; June 14 2013. Published in Journal of Integer Sequences, July 25 2013.

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