integer n (in this sequence, we define s(0) = 0). It remains unknown whether these sequences always end with a prime number, a perfect number, or a periodic sequence of sociable numbers. See also Divisor function: The sum of the (xth powers of the) positive divisors of a number William of Auberive, medieval numerologist interested in aliquot sums References External links Arithmetic dynamics Arithmetic functions Divisor function Perfect numbers