{
  "abstract": "We introduce a broad generalization of a recursive formula for the Möbius function $μ(n) = 1-n-\\sum_{d=2}^{n-1}μ(d)\\left[\\frac{n}{d}\\right]$ due to George Spencer-Brown. By replacing the greatest integer function $\\left[\\frac{n}{d}\\right]$ in this classical recurrence with an arbitrary arithmetic function $f\\left(\\left[\\frac{n}{d}\\right]\\right)$ with $f(1)=1$, we define a new generalized family of functions, denoted $\\star(n)$. We prove that $\\star(p) = -1$ if and only if $p$ is prime. This result yields a surprising algebraic characterization of primes and reveals a deep structural property underlying divisor sums and the greatest integer function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25628",
  "author_total": 3,
  "authors": [
    {
      "name": "George E. Andrews"
    },
    {
      "name": "Louis H. Kauffman"
    },
    {
      "name": "Divyamaan Sahoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87mnz236fhwv1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25628",
  "fulltext_url": null,
  "id": "87mnz236fhwv1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25628",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214094283",
  "pdf_url": "https://arxiv.org/pdf/2609.25628",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87mnz236fhwv1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25628",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25628"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A surprising generalization of the Möbius function",
  "title_text": "A surprising generalization of the Möbius function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/87mnz236fhwv1",
  "venue": "arXiv",
  "versions": []
}