Odd Amicable Pair/Sequence

Sequence

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

$\tuple {12285, 14595}, \tuple {67095, 71145}, \tuple {69615, 87633}, \tuple {100485, 124155}, \ldots$

This sequence is A262623 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Examples

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

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

$\map {\sigma_1} {12 \, 285} = \map {\sigma_1} {14 \, 595} = 26 \, 880 = 12 \, 285 + 14 \, 595$

$67 \, 095$ and $71 \, 145$

Odd Amicable Pair/Examples/67,095-71,145

$69 \, 615$ and $87 \, 633$

Odd Amicable Pair/Examples/69,615-87,633

$100 \, 485$ and $124 \, 155$

Odd Amicable Pair/Examples/100,485-124,155

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

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

$\map {\sigma_1} {1 \, 175 \, 265} = \map {\sigma_1} {1 \, 438 \, 983} = 2 \, 614 \, 240 = 1 \, 175 \, 265 + 1 \, 438 \, 983$

Sources

• Weisstein, Eric W. "Amicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicablePair.html