Journal of Integer Sequences, Vol. 20 (2017), Article 17.7.4

The rth Moment of the Divisor Function: An Elementary Approach

Florian Luca
School of Mathematics
University of the Witwatersrand
Private Bag 3, Wits 2050
South Africa
Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn
Department of Mathematics
Faculty of Sciences
University of Ostrava
30 dubna 22
701 03 Ostrava 1
Czech Republic

László Tóth
Department of Mathematics
University of Pécs
Ifjúság útja 6
H-7624 Pécs


For integer r ≥ 1 we give an elementary proof for the main term of the asymptotic behavior of the rth moment of the number of divisors of n for positive integers nx.

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(Concerned with sequence A000005.)

Received March 20 2017; revised versions received June 27 2017; June 28 2017. Published in Journal of Integer Sequences, July 2 2017.

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