Sociable numbers are similar to
amicable numbers. A chain of numbers is
sociable if the sum of the proper divisors of
each number is the next number in the chain, the last number preceding
the first. The first two chains were found by Poulet in 1918.
The first chain contains five members,

These two chains were the only known sociable chains until 1969, when Henri Cohen used a computer to check all numbers below 60,000,000, and he discovered seven new chains of four links. More have been found since then.

Perfect numbers and amicable numbers could be considered special cases of sociable numbers. A perfect number could be considered as a chain of length 1, while amicable numbers could be seen as a chain of length 2. Curiously, no chains with just three links (which someone named "crowds") have been found.

This process of traversing sociable chains is somewhat reminiscent of looping. See also aliquot chains.