Aliquot Cycle

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).

See also

Aliquot Sequence, Amicable Pair, Sociable Numbers

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Cite this as:

Weisstein, Eric W. "Aliquot Cycle." From MathWorld--A Wolfram Web Resource.

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