Functiones et Approximatio Commentarii Mathematici

Arithmetic functions and their coprimality

Jean-Marie De Koninck and Imre Kátai

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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 $\mbox{gcd}(g(n),f(n-1))=1$.

Article information

Funct. Approx. Comment. Math., Volume 45, Number 1 (2011), 55-66.

First available in Project Euclid: 26 September 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors
Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas 11N37: Asymptotic results on arithmetic functions

arithmetic functions number of divisors sum of divisors shifted primes


De Koninck, Jean-Marie; Kátai, Imre. Arithmetic functions and their coprimality. Funct. Approx. Comment. Math. 45 (2011), no. 1, 55--66. doi:10.7169/facm/1317045231.

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