Odd Amicable Pair/Sequence

Sequence

The sequence of amicable pairs where both terms are odd begins:

$\left({12285, 14595}\right), \left({67095, 71145}\right), \left({69615, 87633}\right), \left({100485, 124155}\right), \ldots$

Examples

$12 \, 285$ and $14 \, 595$

$12 \, 285$ and $14 \, 595$ are the $7$th amicable pair and the smallest odd amicable pair:

$\map \sigma {12 \, 285} = \map \sigma {14 \, 595} = 26 \, 880 = 12 \, 285 + 14 \, 595$

$1 \, 175 \, 265$ and $1 \, 438 \, 983$

$1 \, 175 \, 265$ and $1 \, 438 \, 983$ are the $9$th odd amicable pair:

$\map \sigma {1 \, 175 \, 265} = \map \sigma {1 \, 438 \, 983} = 2 \, 614 \, 240 = 1 \, 175 \, 265 + 1 \, 438 \, 983$