Sociable Chain/Examples/12,496

Example of Sociable Chain
The sociable chain whose smallest element is $12 \, 496$ is of order $5$.

Proof
Let $s \left({n}\right)$ denote the aliquot sum of $n$.

By definition:
 * $s \left({n}\right) = \sigma \left({n}\right) - n$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function.

Thus: