Odd Amicable Pair/Examples/31,695,652,275-33,100,200,525

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Example of Odd Amicable Pair

$31 \, 695 \, 652 \, 275$ and $33 \, 100 \, 200 \, 525$ are an odd amicable pair:

$\map {\sigma_1} {31 \, 695 \, 652 \, 275} = \map {\sigma_1} {33 \, 100 \, 200 \, 525} = 64 \, 795 \, 852 \, 800 = 31 \, 695 \, 652 \, 275 + 33 \, 100 \, 200 \, 525$


Proof

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

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

where $\sigma_1$ denotes the divisor sum function.


Thus:

\(\ds \map {\sigma_1} {31 \, 695 \, 652 \, 275}\) \(=\) \(\ds 64 \, 795 \, 852 \, 800\) $\sigma_1$ of $31 \, 695 \, 652 \, 275$
\(\ds \) \(=\) \(\ds 31 \, 695 \, 652 \, 275 + 33 \, 100 \, 200 \, 525\)
\(\ds \) \(=\) \(\ds \map {\sigma_1} {33 \, 100 \, 200 \, 525}\) $\sigma_1$ of $33 \, 100 \, 200 \, 525$

$\blacksquare$


Sources

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