====== Aliquot sequences ======

Aliquot sequences are defined thus :

>The aliquot sequence starting with a positive integer //k// can be defined formally in terms of the sum-of-divisors function σ<sub>1</sub> or the aliquot sum function //s// in the following way:\\ //s<sub>0</sub> = k//\\ //s<sub>n</sub> = s(s<sub>n−1</sub>) = σ<sub>1</sub>(s<sub>n−1</sub>) − s<sub>n−1</sub> if s<sub>n−1</sub> > 0//\\ //s<sub>n</sub> = 0 if s<sub>n−1</sub> = 0//\\ (if we add this condition, then the terms after 0 are all 0, and all aliquot sequences would be infinite sequence, and we can conjecture that all aliquot sequences are convergent, the limit of these sequences are usually 0 or 6) and s(0) is undefined.\\ \\ Source : [[https://en.wikipedia.org/wiki/Aliquot_sequence|Wikipedia]]

It's conjectured - but not yet proved - that all aliquot sequences will eventually terminate.

All sequences so far tested do terminate - but it nevertheless remains unknown if //all //examples will.