Paolo Starni recently uploaded the preprint titled "On Dris Conjecture about Odd Perfect Numbers", with details below:
Abstract
The Euler's form of odd perfect numbers, if any, is $n = {{\pi}^{\alpha}} N^2$, where $\pi$ is prime, $\gcd(\pi, N) = 1$ and $\pi \equiv \alpha \equiv 1 \pmod 4$. Dris conjecture states that $N > {\pi}^{\alpha}$. We find that $N^2 > \frac{1}{2}{{\pi}^{\gamma}}$, with $\gamma = \max\{\omega(n) - 1, \alpha\}$; $\omega(n) \geq 9$ is the number of distinct prime factors of $n$.
