{
  "id": "0707.4090",
  "version": "v1",
  "published": "2007-07-27T11:53:01.000Z",
  "updated": "2007-07-27T11:53:01.000Z",
  "title": "On some properties of $σ(N)$",
  "authors": [
    "Tomohiro Yamada"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show asymptotic upper and lower bounds for the greatest common divisor of N and $\\sigma(N)$. We also show that there are infinitely many integers N with fairly large g.c.d. of N and $\\sigma(N)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-27T11:53:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11A25"
    ],
    "keywords": [
      "properties",
      "greatest common divisor",
      "asymptotic upper",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4090Y"
    }
  }
}