Amicable Pair/Examples/10,744-10,856
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Example of Amicable Pair
$10 \, 744$ and $10 \, 856$ are the $6$th amicable pair:
- $\map {\sigma_1} {10 \, 744} = \map {\sigma_1} {10 \, 856} = 21 \, 600 = 10 \, 744 + 10 \, 856$
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:
\(\ds \map {\sigma_1} {10 \, 744}\) | \(=\) | \(\ds 21 \, 600\) | $\sigma_1$ of $10 \, 744$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 10 \, 744 + 10 \, 856\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \map {\sigma_1} {10 \, 856}\) | $\sigma_1$ of $10 \, 856$ |
$\blacksquare$
Sources
- Weisstein, Eric W. "Amicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicablePair.html