Definition:Sociable Chain/Order

Definition
Let $m$ be a positive integer.

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

Let a sequence $\left\langle{a_k}\right\rangle$ be a sociable chain. The order of $a_k$ is the smallest $r \in \Z_{>0}$ such that
 * $a_r = a_0$