If an aliquot sequence {s^0(n), s(n), s^2(n), ...} for a given n is bounded, it either ends at s(1) = 0 or becomes periodic. If the sequence is periodic (or eventually periodic), it is known as an aliquot cycle. An aliquot cycle may correspond to a perfect number (period length 1), aspiring number (eventual period length 1), amicable pair (eventual period length 2), or sociable numbers (eventual period length >2).

aliquot sequence | amicable pair | sociable numbers