Aliquot Cycle

If an aliquot sequence ${s^0(n),s(n),s^2(n),...}$ for a given is bounded, it either ends at 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 ).