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
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Authors and affiliations

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


The Euler’s form of odd perfect numbers, if any, is n = παN2, where π is prime, (π, N) = 1 and πα ≡ 1 (mod 4). Dris conjecture states that N > πα. We find that N2 > 1/2 πγ, with γ = max{ω(n) − 1, α}; ω(n) ≥ 10 is the number of distinct prime factors of n.


  • Odd perfect numbers
  • Dris conjecture

2010 Mathematics Subject Classification

  • 11A05
  • 11A25


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Related papers

  1. Dris, J. A. B., & San Diego, I. T. (2020). Some modular considerations regarding odd perfect numbers – Part II. Notes on Number Theory and Discrete Mathematics, 26 (3), 8-24.
  2. Dagal, K. A. P., & Dris, J. A. B. (2021). The abundancy index of divisors of odd perfect numbers – Part II. Notes on Number Theory and Discrete Mathematics, 27(2), 12-19.

Cite this paper

Starni, P. (2018). On Dris conjecture about odd perfect numbers. Notes on Number Theory and Discrete Mathematics, 24(1), 5-9, doi: 10.7546/nntdm.2018.24.1.5-9.

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