Amicable Pair/Examples/6232-6368

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Example of Amicable Pair

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

$\map \sigma {6232} = \map \sigma {6368} = 12 \, 600 = 6232 + 6368$


Proof

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

$\map \sigma m = \map \sigma n = m + n$

where $\sigma$ denotes the $\sigma$ function.


Thus:

\(\ds \map \sigma {6232}\) \(=\) \(\ds 12 \, 600\) $\sigma$ of $6232$
\(\ds \) \(=\) \(\ds 6232 + 6368\)
\(\ds \) \(=\) \(\ds \map \sigma {6368}\) $\sigma$ of $6368$

$\blacksquare$


Sources