Publications de l'Institut Mathématique, Nouvelle SérieVol. 87(101), pp. 121–128 (2010)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 87(101), pp. 121–128 (2010) |
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ON THE COPRIMALITY OF SOME ARITHMETIC FUNCTIONSJean-Marie De Koninck and Imre KataiDép. de mathématiques et de statistique, Université Laval, Québec, Québec G1V 0A6, Canada and Computer Algebra Department, Eötvös Lorand University, 1117 Budapest, Pazmany Péter Sétany I/C, HungaryAbstract: Let $\varphi$ stand for the Euler function. Given a positive integer $n$, let $\sigma(n)$ stand for the sum of the positive divisors of $n$ and let $\tau(n)$ be the number of divisors of $n$. We obtain an asymptotic estimate for the counting function of the set $\{n:\gcd(\varphi(n),\tau(n))=\gcd(\sigma(n),\tau(n))=1\}$. Moreover, setting $l(n):=\gcd(\tau(n),\tau(n+1))$, we provide an asymptotic estimate for the size of $#\{n\leq x:l(n)=1\}$. Keywords: Arithmetic functions, number of divisors, sum of divisors Classification (MSC2000): 11A05, 11A25, 11N37 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Apr 2010. This page was last modified: 18 Jan 2016.
© 2010 Mathematical Institute of the Serbian Academy of Science and Arts
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