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On the number of prime factors of an odd perfect number
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.
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01263897
Contributor : Pascal Ochem <>
Submitted on : Thursday, January 28, 2016 - 1:42:50 PM
Last modification on : Saturday, September 11, 2021 - 3:18:24 AM
Contributor : Pascal Ochem <>
Submitted on : Thursday, January 28, 2016 - 1:42:50 PM
Last modification on : Saturday, September 11, 2021 - 3:18:24 AM
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