Definition:Aliquot Sequence

Definition
Let $m$ be a positive integer.

Let $s \left({m}\right)$ be the aliquot sum of $m$.

Define the sequence $\left\langle{a_k}\right\rangle$ recursively as:
 * $a_{k + 1} = \begin{cases} m & : k = 0 \\ s \left({a_k}\right) & : k > 0 \end{cases}$

The sequence $\left\langle{a_k}\right\rangle$ is known as an aliquot sequence.