On the number of prime factors of an odd perfect number
On the number of prime factors of an odd perfect number
Let $\Omega (n)$ and $\omega (n)$ denote, respectively, the total number of prime factors and the number of distinct prime factors of the integer $n$. Euler proved that an odd perfect number $N$ is of the form $N=p^em^2$ where $p\equiv e\equiv 1\pmod 4$, $p$ is prime, and $p\nmid m$. This …