Multiamicable numbers

Cohen, Graeme L.; Gretton, Stephen F.; Hagis, Peter

doi:10.1090/S0025-5718-1995-1308449-6

Multiamicable numbers
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by Graeme L. Cohen, Stephen F. Gretton and Peter Hagis PDF

Math. Comp. 64 (1995), 1743-1753 Request permission

Abstract:

Multiamicable numbers are a natural generalization of amicable numbers: two numbers form a multiamicable pair if the sum of the proper divisors of each is a multiple of the other. Many other generalizations have been considered in the past. This paper reviews those earlier generalizations and gives examples and properties of multiamicable pairs. It includes a proof that the set of all multiamicable numbers has density 0.

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