Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 in the following way: s0 = k sn = σ1(sn−1) − sn−1.