{
  "id": "0903.1743",
  "version": "v4",
  "published": "2009-03-10T12:00:36.000Z",
  "updated": "2009-03-23T21:37:37.000Z",
  "title": "A recursion for divisor function over divisors belonging to a prescribed finite sequence of positive integers and a solution of the Lahiri problem for divisor function $σ_x(n)$",
  "authors": [
    "Vladimir Shevelev"
  ],
  "comment": "11 pages, improvement of the text of Introduction; addition of Section 5",
  "categories": [
    "math.NT"
  ],
  "abstract": "For a finite sequence of positive integers $A=\\{a_j\\}_{j=1}^{k},$ we prove a recursion for divisor function $\\sigma_{x}^{(A)}(n)=\\sum_{d|n,\\enskip d\\in A}d^x.$ As a corollary, we give an affirmative solution of the problem posed in 1969 by D. B. Lahiri [3]: to find an identity for divisor function $\\sigma_x(n)$ similar to the classic pentagonal recursion in case of $x=1.$",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-03-23T21:37:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37"
    ],
    "keywords": [
      "divisor function",
      "prescribed finite sequence",
      "positive integers",
      "lahiri problem",
      "divisors belonging"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1743S"
    }
  }
}