Amicable Triplet/Examples/1980-2016-2556

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Example of Amicable Triplet

$\left({1980, 2016, 2556}\right)$ form an amicable triplet.


Proof

We have

\(\displaystyle \sigma \left({1980}\right)\) \(=\) \(\displaystyle 6552\) $\sigma$ of $1980$
\(\displaystyle \sigma \left({2016}\right)\) \(=\) \(\displaystyle 6552\) $\sigma$ of $2016$
\(\displaystyle \sigma \left({2556}\right)\) \(=\) \(\displaystyle 6552\) $\sigma$ of $2556$
\(\displaystyle \) \(=\) \(\displaystyle 1980 + 2016 + 2556\)

Hence the result, by definition of amicable triplet.

$\blacksquare$


Sources