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:

$\sigma \left({31 \, 695 \, 652 \, 275}\right) = \sigma \left({33 \, 100 \, 200 \, 525}\right) = 64 \, 795 \, 852 \, 800 = 31 \, 695 \, 652 \, 275 + 33 \, 100 \, 200 \, 525$


Proof

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

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

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


Thus:

\(\displaystyle \sigma \left({31 \, 695 \, 652 \, 275}\right)\) \(=\) \(\displaystyle 64 \, 795 \, 852 \, 800\) $\sigma$ of $31 \, 695 \, 652 \, 275$
\(\displaystyle \) \(=\) \(\displaystyle 31 \, 695 \, 652 \, 275 + 33 \, 100 \, 200 \, 525\)
\(\displaystyle \) \(=\) \(\displaystyle \sigma \left({33 \, 100 \, 200 \, 525}\right)\) $\sigma$ of $33 \, 100 \, 200 \, 525$

$\blacksquare$


Sources