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

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

where $\map {\sigma_1} n$ denotes the divisor sum function.

Thus:

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