Journal of Integer Sequences, Vol. 13 (2010), Article 10.3.7

Some Arithmetic Functions Involving Exponential Divisors

Xiaodong Cao
Department of Mathematics and Physics
Beijing Institute of Petro-Chemical Technology
Beijing, 102617
P. R. China

Wenguang Zhai
School of Mathematical Sciences
Shandong Normal University
Jinan, 250014
P. R. China


In this paper we study several arithmetic functions connected with the exponential divisors of integers. We establish some asymptotic formulas under the Riemann hypothesis, which improve previous results. We also prove some asymptotic lower bounds.

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Received January 29 2010; revised versions received March 10 2010. Published in Journal of Integer Sequences, March 12 2010.

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