{
  "id": "1803.00324",
  "version": "v1",
  "published": "2018-03-01T12:00:43.000Z",
  "updated": "2018-03-01T12:00:43.000Z",
  "title": "Primitive weird numbers having more than three distinct prime factors",
  "authors": [
    "Gianluca Amato",
    "Maximilian F. Hasler",
    "Giuseppe Melfi",
    "Maurizio Parton"
  ],
  "journal": "Riv. Mat. Univ. Parma, 7(1), (2016), 153-163",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield primitive weird numbers of the form $mp_1\\dots p_k$ for a suitable deficient positive integer $m$ and primes $p_1,\\dots,p_k$ and generalize a recent technique developed for generating primitive weird numbers of the form $2^np_1p_2$. The same techniques can be used to search for odd weird numbers, whose existence is still an open question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-01T12:00:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11B83"
    ],
    "keywords": [
      "distinct prime factors",
      "algorithms yield primitive weird numbers",
      "odd weird numbers",
      "suitable deficient positive integer",
      "sufficient conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}