Define the abundancy Σ(n) of a positive integer n as Σ(n) congruent (σ(n))/n, where σ(n) is the divisor function. Then a pair of distinct numbers (k, m) is a friendly pair (and k is said to be a friend of m) if their abundancies are equal: Σ(k) = Σ(m). For example, (4320, 4680) is a friendly pair since σ(4320) = 15120, σ(4680) = 16380, and Σ(4320) | congruent | 15120/4320 = 7/2 Σ(4680) | congruent | 16380/4680 = 7/2.

abundancy | aliquot sequence | amicable pair | friend | friendly number | solitary number