EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 87(101), pp. 121–128 (2010)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror



Jean-Marie De Koninck and Imre Katai

Dép. 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, Hungary

Abstract: 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: 14 May 2010.

© 2010 Mathematical Institute of the Serbian Academy of Science and Arts
© 2010 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition