An improvement of an inequality of Ochem and Rao concerning odd perfect numbers
Abstract
Let $\Omega(n)$ denote the total number of prime divisors of $n$ (counting multiplicity) and let $\omega(n)$ denote the number of distinct prime divisors of $n$. Various inequalities have been proved relating $\omega(N)$ and $\Omega(N)$ when $N$ is an odd perfect number. We improve on these inequalities. In particular, we show that if $3 \not N$, then $\Omega \geq \frac{8}{3}\omega(N)\frac{7}{3}$ and if $3 N$ then $\Omega(N) \geq \frac{21}{8}\omega(N)\frac{39}{8}.$
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.07009
 Bibcode:
 2017arXiv170607009Z
 Keywords:

 Mathematics  Number Theory;
 11A05 (Primary);
 11A25 (Secondary)
 EPrint:
 6 pages, accepted to INTEGERS