Amicable Pair/Examples/220-284

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

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

By definition:
 * $\map s n = \map \sigma n - n$

where $\map \sigma n$ 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.