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

Example of Odd Amicable Pair
$12 \, 285$ and $14 \, 595$ are the $7$th amicable pair and the smallest odd amicable pair:
 * $\map \sigma {12 \, 285} = \map \sigma {14 \, 595} = 26 \, 880 = 12 \, 285 + 14 \, 595$

Proof
By definition, $m$ and $n$ form an amicable pair :
 * $\map \sigma m = \map \sigma n = m + n$

where $\map \sigma n$ 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.