Matchable numbers

Abstract: We say a natural number is matchable if there is a bijection from the set of $\tau(n)$ divisors of $n$ to the set $[1,2,\ldots,\tau(n)]$, 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. This is joint work with Carl Pomerance.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)