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