Journal of Integer Sequences, Vol. 23 (2020), Article 20.9.8

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 abN . 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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