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arXiv · 1706.02144

On Dris Conjecture about Odd Perfect Numbers

Paolo Starni
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Abstract

The Euler's form of odd perfect numbers, if any, is $n=π^αN^2$, where $π$ is prime, $(π,N)=1$ and $π\equiv α\equiv 1 \pmod{4}$. Dris conjecture states that $N>π^α$. We find that $N^2>\frac{1}{2}π^γ$, with $γ=max\{ω(n)-1,α\}$; $ω(n)\geq 9$ is the number of distinct prime factors of $n$.

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Paolo Starni. 2017-06-07. On Dris Conjecture about Odd Perfect Numbers. https://arxiv.org/abs/1706.02144

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