A generalisation of the concept of
amicable numbers, a sociable (or social) chain is an
aliquot sequence which repeats with a period greater than 2. For example, if we begin with 14288 we obtain a chain of length 5, the other members being 15472, 14536, 14264 and 12496. ("Chains" of length 2 are called
amicable and of length 1
perfect.)
Sociable chains are also known as aliquot cycles.