Amicable Pair/Examples/6232-6368

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Example of Amicable Pair

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

$\map {\sigma_1} {6232} = \map {\sigma_1} {6368} = 12 \, 600 = 6232 + 6368$


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 $\sigma_1$ denotes the divisor sum function.


Thus:

\(\ds \map {\sigma_1} {6232}\) \(=\) \(\ds 12 \, 600\) $\sigma_1$ of $6232$
\(\ds \) \(=\) \(\ds 6232 + 6368\)
\(\ds \) \(=\) \(\ds \map {\sigma_1} {6368}\) $\sigma_1$ of $6368$

$\blacksquare$


Sources