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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## 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 ^{α}N*

^{2}, where

*π*is prime, (

*π*,

*N*) = 1 and

*π*≡

*α*≡ 1 (mod 4). Dris conjecture states that

*N*>

*π*. We find that

^{α}*N*

^{2}> 1/2

*π*, with

^{γ}*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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## Related papers

- 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.
- 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.