The abundancy index of divisors of odd perfect numbers: Part II

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Notes on Number Theory and Discrete Mathematics

Volume

27

Issue

2

First Page

12

Last Page

19

Publication Date

2021

Abstract

In this note, we show that if N = q kn 2 is an odd perfect number with special prime q, and N is not divisible by 3, then the inequality q < n holds. We then give another unconditional proof for the inequality q < n which is independent of the results of Brown and Starni.

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Digitial Object Identifier (DOI)

10.7546/nntdm.2021.27.2.12-19

Disciplines

Mathematics

Keywords

Perfect numbers; Numbers, Prime

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