Skip to Main content Skip to Navigation
Journal articles

On the number of prime factors of an odd perfect number

Pascal Ochem 1 Michael Rao 2 
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 MC2 - Modèles de calcul, Complexité, Combinatoire
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Let ω(n) and Ω(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 = pᶱm² where p ≡ e ≡ 1 (mod 4), p is prime, and p ∤ m. This implies that Ω(N) ≥ 2ω(N) − 1. We. We prove that Ω(N) ≥ (18ω(N) −31) / 7andΩ(N) ≥ 2ω(N) + 51.
Document type :
Journal articles
Complete list of metadata
Contributor : Pascal Ochem Connect in order to contact the contributor
Submitted on : Thursday, January 28, 2016 - 1:42:50 PM
Last modification on : Friday, August 5, 2022 - 3:02:53 PM

Links full text



Pascal Ochem, Michael Rao. On the number of prime factors of an odd perfect number. Mathematics of Computation, American Mathematical Society, 2014, 83 (289), pp.2435-2439. ⟨10.1090/S0025-5718-2013-02776-7⟩. ⟨lirmm-01263897⟩



Record views