Amicable Pair/Examples/220-284

Example of Amicable Pair
$220$ and $284$ are the smallest amicable pair:
 * $\map {\sigma_1} {220} = \map {\sigma_1} {284} = 504 = 220 + 284$

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