Odd Amicable Pair/Examples/1,175,265-1,438,983

Example of Odd Amicable Pair

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

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

By definition, $m$ and $n$ form an amicable pair if and only if:

$\map {\sigma_1} m = \map {\sigma_1} n = m + n$

where $\map {\sigma_1} n$ denotes the divisor sum function.

Thus:

$\ds \map {\sigma_1} {1 \, 175 \, 265}$

$=$

$\ds 2 \, 614 \, 240$

$\ds $

$=$

$\ds 1 \, 175 \, 265 + 1 \, 438 \, 983$

$\ds $

$=$

$\ds \map {\sigma_1} {1 \, 438 \, 983}$

$\blacksquare$

The odd amicable pair $1 \, 175 \, 265$ and $1 \, 438 \, 983$ was discovered by G.W. Kraft in the $17$th century.

It was the $1$st odd amicable pair to be discovered.