{
  "id": "1706.07009",
  "version": "v1",
  "published": "2017-06-21T16:59:49.000Z",
  "updated": "2017-06-21T16:59:49.000Z",
  "title": "An improvement of an inequality of Ochem and Rao concerning odd perfect numbers",
  "authors": [
    "Joshua Zelinsky"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "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 $\\Omega(N) \\geq \\frac{21}{8}\\omega(N)-\\frac{39}{8}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T16:59:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11A25"
    ],
    "keywords": [
      "rao concerning odd perfect numbers",
      "inequality",
      "improvement",
      "distinct prime divisors",
      "total number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}