{
  "id": "1103.1090",
  "version": "v14",
  "published": "2011-03-05T23:34:43.000Z",
  "updated": "2012-08-03T14:05:57.000Z",
  "title": "The Abundancy Index of Divisors of Odd Perfect Numbers",
  "authors": [
    "Jose Arnaldo B. Dris"
  ],
  "comment": "10 pages",
  "journal": "Journal of Integer Sequences, Vol. 15 (2012), Article 12.4.4 - Available online at <https://cs.uwaterloo.ca/journals/JIS/VOL15/Dris/dris8.html>",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $N = {q^k}{n^2}$ is an odd perfect number, where $q$ is the Euler prime, then we show that $n < q$ is sufficient for Sorli's conjecture that $k = \\nu_{q}(N) = 1$ to hold. We also prove that $q^k < 2/3{n^2}$, and that $I(q^k) < I(n)$, where $I(x)$ is the abundancy index of $x$.",
  "revisions": [
    {
      "version": "v14",
      "updated": "2012-08-03T14:05:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11J25",
      "11J99"
    ],
    "keywords": [
      "odd perfect number",
      "abundancy index",
      "euler prime",
      "sorlis conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1090D"
    }
  }
}