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ON SUMS INVOLVING THE EULER TOTIENT FUNCTION
Part of
- Elementary number theory
- Multiplicative number theory
ISAO KIUCHI, YUKI TSURUTA
Journal:

Bulletin of the Australian Mathematical Society / Volume 109 / Issue 3 / June 2024

Published online by Cambridge University Press:

24 August 2023, pp. 486-497

Print publication:

June 2024
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Let $\gcd (n_{1},\ldots ,n_{k})$ denote the greatest common divisor of positive integers $n_{1},\ldots ,n_{k}$ and let $\phi $ be the Euler totient function. For any real number $x>3$ and any integer $k\geq 2$, we investigate the asymptotic behaviour of $\sum _{n_{1}\ldots n_{k}\leq x}\phi (\gcd (n_{1},\ldots ,n_{k})). $