<P> In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself . Two numbers with the same abundancy form a friendly pair; n numbers with the same abundancy form a friendly n - tuple . </P> <P> Being mutually friendly is an equivalence relation, and thus induces a partition of the positive naturals into clubs (equivalence classes) of mutually friendly numbers . </P> <P> A number that is not part of any friendly pair is called solitary . </P> <P> The abundancy index of n is the rational number σ (n) / n, in which σ denotes the sum of divisors function . A number n is a friendly number if there exists m ≠ n such that σ (m) / m = σ (n) / n . Note that abundancy is not the same as abundance, which is defined as σ (n) − 2n . </P>

Numbers which do not make pairs are called