Matchable numbers, defined via a coprime bijection between divisors and {1 to tau(n)}, have a positive asymptotic density that the authors compute, and all squarefree numbers are matchable.
McNew, Permutations and the divisor graph of [1, n], Mathematika63(2023), 51–67
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Matchable numbers
Matchable numbers, defined via a coprime bijection between divisors and {1 to tau(n)}, have a positive asymptotic density that the authors compute, and all squarefree numbers are matchable.