Aliquot sequence

An aliquot sequence in mathematics is a recursive sequence which can be defined in the following way: if we write σ(n)=σ₁(n) to be the divisor function normally, then, the aliquot sequence of k can be written:

s₀ = k

s_n = σ(s_n-1) - s_n-1

For example, the aliquot sequence of 10 is 10, 8, 7, 1, 0.

An important conjecture due to Catalan with respect to aliquot sequences is that every aliquot sequence ends in a prime number, perfect number, or a set of sociable numbers.