Summary: Define a quasi-amicable pair as a pair of distinct natural numbers each of which is the sum of the nontrivial divisors of the other, e.g., ${48, 75}$. Here $nontrivial$ excludes both 1 and the number itself. Quasi-amicable pairs have been studied (primarily empirically) by Garcia, Beck and Najar, Lal and Forbes, and Hagis and Lord. We prove that the set of $n$ belonging to a quasi-amicable pair has asymptotic density zero.

11A25, 11N37

aliquot sequence, quasi-aliquot sequence, quasi-amicable pair, augmented amicable pair