aliquot cycle | amicable numbers

Let s(n) congruent σ(n) - n, where σ(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n) congruent n, s^1(n) = s(n), s^2(n) = s(s(n)), ... is called an aliquot sequence. If the sequence for a given n is bounded, it either ends at s(1) = 0 or becomes periodic. 1. If the sequence reaches a constant, the constant is known as a perfect number. A number that is not perfect, but for which the sequence becomes constant, is known as an aspiring number.

196-algorithm | additive persistence | aspiring number | Catalan's aliquot sequence conjecture | multiamicable numbers | multiperfect number | multiplicative persistence | perfect number | sociable numbers | unitary aliquot sequence