The rth Moment of the Divisor Function: An Elementary Approach
Florian Luca
School of Mathematics
University of the Witwatersrand
Private Bag 3, Wits 2050
Johannesburg
South Africa
and
Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn
Germany
and
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
Hungary
Abstract:
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 n ≤ x.
Full version: pdf,
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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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