Report
An improvement of an inequality of Ochem and Rao concerning odd perfect numbers
| العنوان: | An improvement of an inequality of Ochem and Rao concerning odd perfect numbers |
|---|---|
| المؤلفون: | Zelinsky, Joshua |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11A05 (Primary), 11A25 (Secondary) |
| الوصف: | 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 $\Omega(N) \geq \frac{21}{8}\omega(N)-\frac{39}{8}.$ Comment: 6 pages, accepted to INTEGERS |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1706.07009 |
| رقم الانضمام: | edsarx.1706.07009 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |