Amicable Pair/Examples/6232-6368

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Example of Amicable Pair

$6232$ and $6368$ are the $5$th amicable pair:

$\sigma \left({6232}\right) = \sigma \left({6368}\right) = 12 \, 600 = 6232 + 6368$


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:

\(\displaystyle \sigma \left({6232}\right)\) \(=\) \(\displaystyle 12 \, 600\) $\sigma$ of $6232$
\(\displaystyle \) \(=\) \(\displaystyle 6232 + 6368\)
\(\displaystyle \) \(=\) \(\displaystyle \sigma \left({6368}\right)\) $\sigma$ of $6368$

$\blacksquare$


Sources