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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:
∑
n ≤ y ∑
q ≤ x ∑
d | ( n , q ) d f ( q
d )
for any positive real numbers
x
and
y .
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
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Publishers).