{
  "id": "2212.05549",
  "version": "v1",
  "published": "2022-12-11T17:29:07.000Z",
  "updated": "2022-12-11T17:29:07.000Z",
  "title": "On a sum of a multiplicative function linked to the divisor function over the set of integers B-multiple of 5",
  "authors": [
    "Mihoub Bouderbala"
  ],
  "comment": "7pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $d(n)$ and $d^{\\ast}(n)$ be the numbers of divisors and the numbers of unitary divisors of the integer $n\\geq1$. In this paper, we prove that \\[ \\underset{n\\in\\mathcal{B}}{\\underset{n\\leq x}{\\sum}}\\frac{d(n)}{d^{\\ast}% (n)}=\\frac{16\\pi% %TCIMACRO{\\U{b2}}% %BeginExpansion {{}^2}% %EndExpansion }{123}\\underset{p}{\\prod}(1-\\frac{1}{2p% %TCIMACRO{\\U{b2}}% %BeginExpansion {{}^2}% %EndExpansion }+\\frac{1}{2p^{3}})x+\\mathcal{O}\\left( x^{\\frac{\\ln8}{\\ln10}+\\varepsilon }\\right) ,~\\left( x\\geqslant1,~\\varepsilon>0\\right) , \\] where $\\mathcal{B}$ is the set which contains any integer that is not a multiple of $5,$ but some permutations of its digits is a multiple of $5.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-11T17:29:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11N37"
    ],
    "keywords": [
      "divisor function",
      "integers b-multiple",
      "multiplicative function",
      "unitary divisors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}