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On a sum involving squarefull numbers, II

Isao Kiuchi

Vol. 12 (2023), No. 3, 241–246
Abstract

Let (n,q) denote the greatest common divisor of positive integers n and q, and let f denote the characteristic function of squarefull numbers. Then, under the Riemann hypothesis, we shall obtain a more precise asymptotic formula for the following sum involving squarefull numbers:

ny qx d|(n,q)df(q d)

for any positive real numbers x and y.

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Keywords
squarefull numbers, Riemann zeta-function, divisor function, asymptotic results on arithmetical functions, Riemann hypothesis
Mathematical Subject Classification
Primary: 11A25
Secondary: 11N37, 11P99
Milestones
Received: 19 April 2023
Revised: 15 July 2023
Accepted: 1 August 2023
Published: 23 September 2023
Authors
Isao Kiuchi
Department of Mathematical Sciences
Faculty of Science
Yamaguchi University
Yamaguchi
Japan