Conditions equivalent to the Descartes–Frenicle–Sorli Conjecture on odd perfect numbers

Jose Arnaldo B. Dris
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 12–20
Full paper (PDF, 156 Kb)

Details

Authors and affiliations

Jose Arnaldo B. Dris
Department of Mathematics and Physics,
Far Eastern University
Nicanor Reyes Street, Sampaloc, Manila, Philippines

Abstract

The Descartes-Frenicle-Sorli conjecture predicts that k = 1 if q^kn² is an odd perfect number with Euler prime q. In this note, we present some conditions equivalent to this conjecture.

Keywords

• Odd perfect number
• Abundancy index
• Deficiency

AMS Classification

• 11A25

References

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