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
- Weisstein, Eric W. "Amicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicablePair.html