{
  "id": "2411.11404",
  "version": "v1",
  "published": "2024-11-18T09:27:32.000Z",
  "updated": "2024-11-18T09:27:32.000Z",
  "title": "Arithmetic properties of MacMahon-type sums of divisors",
  "authors": [
    "James A. Sellers",
    "Roberto Tauraso"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function $U_t(a,q)$ which is an extension of MacMahon's generalized sum-of-divisors function. As a by-product, we also show that, for all $n\\geq 0$, $\\overline{B}_3(15n+7)\\equiv 0 \\pmod{5}$ where $\\overline{B}_3(n)$ is the number of almost $3$-regular overpartitions of $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-18T09:27:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P83",
      "11P81",
      "05A17"
    ],
    "keywords": [
      "arithmetic properties",
      "macmahon-type sums",
      "macmahons generalized sum-of-divisors function",
      "infinite families",
      "regular overpartitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}