New Existence Results for Odd Perfect Numbers of the Form n = p^α x N^2β

EasyChair Preprint no. 9447

Abstract

Let n be an odd perfect number of the form n = p^αN^2β , where N, β, α are positive integers, N > 2 is square free, p is a prime satisfying p ≡ α ≡ 1 (mod 4) and p∤N. We prove that β ≠ 27, 42.

Keyphrases: divisor function, Eulerian Form, Odd perfect numbers

@Booklet{EasyChair:9447,
  author = {Emmanuel Elima},
  title = {New Existence Results for Odd Perfect Numbers of the Form n = p^α x N^2β},
  howpublished = {EasyChair Preprint no. 9447},

  year = {EasyChair, 2022}}