Odd Amicable Pair/Examples/12,285-14,595

Example of Odd Amicable Pair
$12 \, 285$ and $14 \, 595$ are the smallest odd amicable pair:
 * $\sigma \left({12 \, 285}\right) = \sigma \left({14 \, 595}\right) = 26 \, 880 = 12 \, 285 + 14 \, 595$

Proof
By definition, $m$ and $n$ form an amicable pair :
 * $\sigma \left({m}\right) = \sigma \left({n}\right) = m + n$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function.

Thus:

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