Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the number of prime factors of an odd perfect number
HTML articles powered by AMS MathViewer

by Pascal Ochem and Michaël Rao PDF
Math. Comp. 83 (2014), 2435-2439 Request permission

Abstract:

Let $\Omega (n)$ and $\omega (n)$ denote, respectively, the total number of prime factors and the number of distinct prime factors of the integer $n$. Euler proved that an odd perfect number $N$ is of the form $N=p^em^2$ where $p\equiv e\equiv 1\pmod 4$, $p$ is prime, and $p\nmid m$. This implies that $\Omega (N)\ge 2\omega (N)-1$. We prove that $\Omega (N)\ge (18\omega (N)-31)/7$ and $\Omega (N)\ge 2\omega (N)+51$.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 11A25, 11A51
  • Retrieve articles in all journals with MSC (2010): 11A25, 11A51
Additional Information
  • Pascal Ochem
  • Affiliation: CNRS, LIRMM, Université Montpellier 2, 161 rue Ada, 34095 Montpellier Cedex 5, France
  • Email: ochem@lirmm.fr
  • Michaël Rao
  • Affiliation: CNRS, LIP, ENS Lyon, 15 parvis R. Descartes BP 7000, 69342 Lyon Cedex 07, France
  • MR Author ID: 714149
  • Email: michael.rao@ens-lyon.fr
  • Received by editor(s): September 15, 2012
  • Received by editor(s) in revised form: December 18, 2012
  • Published electronically: November 20, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2435-2439
  • MSC (2010): Primary 11A25, 11A51
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02776-7
  • MathSciNet review: 3223339