Amicable Pair/Examples/220-284

Example of Amicable Pair
$220$ and $284$ are the smallest amicable pair:
 * $\sigma \left({220}\right) = \sigma \left({284}\right) = 504 = 220 + 284$

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 can be determined by inspection of the aliquot sums of all smaller integers that there is no smaller amicable pair.