On Dris Conjecture about Odd Perfect Numbers

Abstract

The Euler's form of odd perfect numbers, if any, is $n={\pi }^{\alpha }{N}^2$, where $\pi$ is prime, $(\pi ,N)=1$ and $\pi \equiv \alpha \equiv 1(\mathrm{mod}4)$. Dris conjecture states that $N>{\pi }^{\alpha }$. We find that $N^2>\frac{1}{2}{\pi }^{\gamma }$, with $\gamma =max\{\omega (n)-1,\alpha \}$; $\omega (n)\ge 9$ is the number of distinct prime factors of $n$.

5 pages

References in corpus (1)

• Odd Multiperfect Numbers