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arXiv · 2512.18424

A Flanking Pattern in a Sum-of-Divisors Congruence

Scott Duke Kominers
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Abstract

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 $S_{k}$.

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Scott Duke Kominers. 2025-12-20. A Flanking Pattern in a Sum-of-Divisors Congruence. https://arxiv.org/abs/2512.18424

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