On sums of sums involving squarefull numbers
Volume 200 / 2021
Acta Arithmetica 200 (2021), 197-211
MSC: Primary 11N37; Secondary 11A25.
DOI: 10.4064/aa201027-8-2
Published online: 27 July 2021
Abstract
For any positive real numbers $x$ and $y$, we shall consider several asymptotic formulas for sums of the modified squarefull numbers, namely $$ S_{k}(x,y):=\sum _{n\leq y}\biggl (\sum _{q\leq x}\sum _{d|(n,q)}df\biggl (\frac {q}{d}\bigg )\bigg )^{k} \quad \ (k=1,2) $$ where $n$ and $q$ are positive integers and $f$ denotes the characteristic function of the squarefull numbers.
