{
  "id": "1011.4262",
  "version": "v1",
  "published": "2010-11-18T19:35:34.000Z",
  "updated": "2010-11-18T19:35:34.000Z",
  "title": "The distribution functions of $σ(n)/n$ and $n/φ(n)$, II",
  "authors": [
    "Andreas Weingartner"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\sigma(n)$ be the sum of the positive divisors of $n$, and let $A(t)$ be the natural density of the set of positive integers $n$ satisfying $\\sigma(n)/n \\ge t$. We give an improved asymptotic result for $\\log A(t)$ as $t$ grows unbounded. The same result holds if $\\sigma(n)/n$ is replaced by $n/\\phi(n)$, where $\\phi(n)$ is Euler's totient function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-18T19:35:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N25",
      "11N60"
    ],
    "keywords": [
      "distribution functions",
      "eulers totient function",
      "natural density",
      "asymptotic result",
      "result holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4262W"
    }
  }
}