aliquot cycle

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted divisor function s(n) = σ(n) - n to n and σ(n) is the usual divisor function. If the period of the aliquot cycle is 1, the number is called a perfect number. If the period is 2, the two numbers are called an amicable pair. In general, if the period is t>=3, the number is called sociable of order t. For example, 1264460 is a sociable number of order four since its aliquot sequence is 1264460, 1547860, 1727636, 1305184, 1264460, ....

aliquot sequence | Catalan's aliquot sequence conjecture | perfect number | unitary sociable numbers