Asymptotic formulae concerning the product and the quotient of the arithmetical functions $σ_S$ and$φ_S$

Rok, strany: 1997, 167 - 175

Let $σ_s(n)$ denote the sum of $s$-powers of the positive divisors of $n$ and let $φ_s(n)=∑_d|nd^sμ(n/d)$ be the generalized Euler function. In this paper we establish asymptotic formulae for $∑_{n\leqslant x}σ_s(n)φ_s(n)$, $∑_{n\leqslant x}σ_s(n)/φ_s(n)$ in case $s>0$ and for $∑_{n\leqslant x}φ_s(n)/σ_s(n)$ in case $s\geqslant 1$.

ISO 690:

Tóth, L. 1997. Asymptotic formulae concerning the product and the quotient of the arithmetical functions $σ_S$ and$φ_S$. In Tatra Mountains Mathematical Publications, vol. 11, no.2, pp. 167-175. 1210-3195.

APA:

Tóth, L. (1997). Asymptotic formulae concerning the product and the quotient of the arithmetical functions $σ_S$ and$φ_S$. Tatra Mountains Mathematical Publications, 11(2), 167-175. 1210-3195.