A Summation Involving the Divisor and GCD Functions
Randell Heyman
School of Mathematics and Statistics
University of New South Wales
High Street
Kensington, N.S.W. 2052
Australia
Abstract:
Let N be a positive integer. Dudek asked for an asymptotic formula
for the sum of τ(gcd(a, b)) for all a and b
with ab ≤ N . We give an asymptotic result. The approach
is partly geometric and differs from the approach used in many recent
gcd-sum results.
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(Concerned with sequences
A268732.)
Received April 1 2020; revised versions received April 19 2020; May 1 2020; June 17 2020;
June 30 2020.
Published in Journal of Integer Sequences,
October 16 2020. Minor corrections, February 6 2021.
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