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On sums of sums involving squarefull numbers

Volume 200 / 2021

Isao Kiuchi 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.

Authors

  • Isao KiuchiDepartment of Mathematical Sciences
    Faculty of Science
    Yamaguchi University
    Yoshida 1677-1, Yamaguchi 753-8512, Japan
    e-mail

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