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Comptes Rendus Mathématique
Volume 340, n° 1
pages 1-4 (janvier 2005)
Doi : 10.1016/j.crma.2004.11.014
Received : 14 September 2004 ;  accepted : 15 November 2004
Sur un problème de S. Ramanujan
On a problem by S. Ramanujan
 

Abdelhakim Smati
Laco, UMR-CNRS 6090, université de Limoges, 123, avenue Albert-Thomas, 87060 Limoges cedex, France 

Résumé

En 1915, Srinivasa Ramanujan donne une borne inférieure de lʼordre maximum de la fonction itérée du nombre des diviseurs,  . En 1989, Paul Erdős et Aleksandar Ivić en donnent une borne supérieure. Dans cette Note, on détermine lʼordre maximum de  , le nombre de diviseurs premiers de  , et on en déduit une amélioration du résultat dʼErdős et Ivić sur lʼordre maximum de  . Pour citer cet article : A. Smati, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.
Abstract

In 1915, Srinivasa Ramanujan gives a lower limit for the maximum order of the iterated of the divisors function,  . In 1989, Paul Erdős and Aleksandar Ivić give a upper bound. In this Note, we find the maximal order of the function  , the number of prime divisors of  , and we improve the result of Erdős and Ivić on the maximal order of  . To cite this article: A. Smati, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.


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