On Dris conjecture about odd perfect numbers

Paolo Starni
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 1, Pages 5–9
DOI: 10.7546/nntdm.2018.24.1.5-9
Full paper (PDF, 141 Kb)

Details

Authors and affiliations

Paolo Starni
School of Economics, Management, and Statistics
Rimini Campus, University of Bologna
Via Anghera 22, 47921 Rimini, Italy

Abstract

The Euler’s form of odd perfect numbers, if any, is n = π^αN², where π is prime, (π, N) = 1 and π ≡ α ≡ 1 (mod 4). Dris conjecture states that N > π^α. We find that N² > 1/2 π^γ, with γ = max{ω(n) − 1, α}; ω(n) ≥ 10 is the number of distinct prime factors of n.

Keywords

• Odd perfect numbers
• Dris conjecture

2010 Mathematics Subject Classification

• 11A05
• 11A25

References

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