On Dris conjecture about odd perfect numbers

Paolo Starni
2018 Notes on Number Theory and Discrete Mathematics  
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 α . We find that N 2 > 1 2 π γ , with γ = max{ω(n) − 1, α}; ω(n) ≥ 10 is the number of distinct prime factors of n.
doi:10.7546/nntdm.2018.24.1.5-9 fatcat:tk2kwpxreranpgfzskjig25p6m