Geodesic
Quasi-amicable numbers are rare
Journal of integer sequences, Tome 14 (2011) no. 5
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.
Classification : 11A25, 11N37
Keywords: aliquot sequence, quasi-aliquot sequence, quasi-amicable pair, augmented amicable pair 
@article{JIS_2011__14_5_a2,
     author = {Pollack,  Paul},
     title = {Quasi-amicable numbers are rare},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {5},
     zbl = {1232.11007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a2/}
}
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Pollack,  Paul. Quasi-amicable numbers are rare. Journal of integer sequences, Tome 14 (2011) no. 5. http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a2/