A Flanking Pattern in a Sum-of-Divisors Congruence

Scott Duke Kominers

A Flanking Pattern in a Sum-of-Divisors Congruence

数论 2025-12-23 v1

作者: Scott Duke Kominers

摘要

We consider composite $n$ satisfying the congruence $n \cdot \sigma_k(n) \equiv 2 \pmod{\phi(n)},$ and show a "flanking" structure: $14$ appears in both $S_{k-1}$ and $S_{k+1}$ whenever certain values of $n$ appear in $S_k$ ; and, moreover, $14$ is the only (nontrivial) case of this property. Along the way, we derive a new characterization of the $n$ that appear in the sets $S_{k}$ .

引用

@article{arxiv.2512.18424,
  title  = {A Flanking Pattern in a Sum-of-Divisors Congruence},
  author = {Scott Duke Kominers},
  journal= {arXiv preprint arXiv:2512.18424},
  year   = {2025}
}

备注

8 pages, 2 tables, plus source code appendix

A Flanking Pattern in a Sum-of-Divisors Congruence

摘要

引用

备注

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