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

Keneth Adrian Precillas Dagal and Jose Arnaldo Bebita Dris
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 12–19
DOI: 10.7546/nntdm.2021.27.2.12-19
Full paper (PDF, 203 Kb)

Details

Authors and affiliations

Keneth Adrian Precillas Dagal
Nasser Vocational Training Centre, Bahrain

Jose Arnaldo Bebita Dris
M. Sc. Graduate, Mathematics Department
De La Salle University, Manila 1004, Philippines

Abstract

In this note, we show that if N = q^kn² 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.

Keywords

• Descartes–Frenicle–Sorli conjecture
• Odd perfect number
• Special prime
• Abundancy index

2020 Mathematics Subject Classification

• 11A05
• 11A25

References

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