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arXiv · 2604.05304

Matchable numbers

Nathan McNew·Carl Pomerance
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Abstract

We say a natural number $n$ is matchable if there is a bijection from the set of $\tau(n)$ divisors of $n$ to the set $\{1,2,\dots,\tau(n)\}$, where corresponding numbers are relatively prime. We show that the set of matchable numbers has an asymptotic density, which we compute, and we show that every squarefree number is matchable. We also present some related unsolved problems.

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Nathan McNew, Carl Pomerance. 2026-04-07. Matchable numbers. https://arxiv.org/abs/2604.05304

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