{
  "id": "1912.11587",
  "version": "v1",
  "published": "2019-12-25T03:50:41.000Z",
  "updated": "2019-12-25T03:50:41.000Z",
  "title": "When the Large Divisors of a Natural Number Are in Arithmetic Progression",
  "authors": [
    "Hung Viet Chu"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Iannucci considered the positive divisors of a natural number $n$ that do not exceed the square root of $n$ and found all numbers whose such divisors are in arithmetic progression. Continuing the work, we define large divisors to be divisors at least $\\sqrt{n}$ and find all numbers whose large divisors are in arithmetic progression. The asymptotic formula for the count of these numbers up to a bound $x$ is observed to be $\\frac{x\\log\\log x}{\\log x}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-25T03:50:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B25"
    ],
    "keywords": [
      "arithmetic progression",
      "natural number",
      "define large divisors",
      "square root",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}