Sociable Chain/Examples/12,496

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

It goes:
 * $12 \, 496 \to 14 \, 288 \to 15 \, 472 \to 14 \, 536 \to 14 \, 264 \to 12 \, 496$

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:

It is interesting to list the prime decomposition of each of the terms in the chain: