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:

$\sigma \left({32 \, 129 \, 958 \, 525}\right) = \sigma \left({32 \, 665 \, 894 \, 275}\right) = 64 \, 795 \, 852 \, 800 = 32 \, 129 \, 958 \, 525 + 32 \, 665 \, 894 \, 275$


Proof

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

$\sigma \left({m}\right) = \sigma \left({n}\right) = m + n$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function.


Thus:

\(\displaystyle \sigma \left({32 \, 129 \, 958 \, 525}\right)\) \(=\) \(\displaystyle 64 \, 795 \, 852 \, 800\) $\sigma$ of $32 \, 129 \, 958 \, 525$
\(\displaystyle \) \(=\) \(\displaystyle 32 \, 129 \, 958 \, 525 + 32 \, 665 \, 894 \, 275\)
\(\displaystyle \) \(=\) \(\displaystyle \sigma \left({32 \, 665 \, 894 \, 275}\right)\) $\sigma$ of $32 \, 665 \, 894 \, 275$

$\blacksquare$


Sources