# Definition:Sociable Chain/Order

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
$a_r = a_0$