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 $\map s n$ denote the aliquot sum of $n$.

By definition:
 * $\map s n = \map {\sigma_1} n - n$

where $\sigma_1$ denotes the divisor sum function.

Thus:

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