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September 2011 Arithmetic functions and their coprimality
Jean-Marie De Koninck, Imre Kátai
Funct. Approx. Comment. Math. 45(1): 55-66 (September 2011). DOI: 10.7169/facm/1317045231

Abstract

Let $D\ge 3$ be an odd integer and $\ell\ge -1$ be a non zero integer such that gcd$(\ell,D)=1$. Let $f,g:\mathbb{N} \to \mathbb{N}$ be multiplicative functions such that $f(p)=D$ and $g(p)=p+\ell$ for each prime $p$. We estimate the number of positive integers $n\le x$ such that gcd$(f(n),g(n))=1$. If $D$ is a prime larger than 3, we also examine the size of the number of positive integers $n\le x$ for which $\mbox{gcd}(g(n),f(n-1))=1$.

Citation

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Jean-Marie De Koninck. Imre Kátai. "Arithmetic functions and their coprimality." Funct. Approx. Comment. Math. 45 (1) 55 - 66, September 2011. https://doi.org/10.7169/facm/1317045231

Information

Published: September 2011
First available in Project Euclid: 26 September 2011

zbMATH: 1261.11062
MathSciNet: MR2865412
Digital Object Identifier: 10.7169/facm/1317045231

Subjects:
Primary: 11A05
Secondary: 11A25, 11N37

Rights: Copyright © 2011 Adam Mickiewicz University

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Vol.45 • No. 1 • September 2011
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