Sociable Chain/Examples/14,316

Example of Sociable Chain
The longest known sociable chain, at time of writing ($9$th March $2017$) is of order $28$.

Its smallest element is $14 \, 316$.

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:

152990, 122410, 97946, 48976, 45946, 22976, 22744, 19916, 17716