Odd Amicable Pair/Examples/32,129,958,525-32,665,894,275

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Example of Odd Amicable Pair

$32 \, 129 \, 958 \, 525$ and $32 \, 665 \, 894 \, 275$ are an odd amicable pair:

$\map {\sigma_1} {32 \, 129 \, 958 \, 525} = \map {\sigma_1} {32 \, 665 \, 894 \, 275} = 64 \, 795 \, 852 \, 800 = 32 \, 129 \, 958 \, 525 + 32 \, 665 \, 894 \, 275$


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


Thus:

\(\ds \map {\sigma_1} {32 \, 129 \, 958 \, 525}\) \(=\) \(\ds 64 \, 795 \, 852 \, 800\) $\sigma_1$ of $32 \, 129 \, 958 \, 525$
\(\ds \) \(=\) \(\ds 32 \, 129 \, 958 \, 525 + 32 \, 665 \, 894 \, 275\)
\(\ds \) \(=\) \(\ds \map {\sigma_1} {32 \, 665 \, 894 \, 275}\) $\sigma_1$ of $32 \, 665 \, 894 \, 275$

$\blacksquare$


Sources