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

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
,
where
*P*(*n*) is the well-known gcd-sum function and
is a fixed integer. In this paper, we use the analytic properties of the Dirichlet divisor function to
obtain the asymptotic formula for it.

(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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