Amicable Pair/Examples/2620-2924

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Example of Amicable Pair

$2620$ and $2924$ are the $3$rd amicable pair:

$\map \sigma {2620} = \map \sigma {2924} = 5544 = 2620 + 2924$


Proof

Let $\map s n$ denote the aliquot sum of $n$.

By definition:

$\map s n = \map \sigma n - n$

where $\map \sigma n$ denotes the $\sigma$ function.


Thus:

\(\displaystyle \map s {2620}\) \(=\) \(\displaystyle \map \sigma {2620} - 2620\)
\(\displaystyle \) \(=\) \(\displaystyle 5544 - 2620\) $\sigma$ of $2620$
\(\displaystyle \) \(=\) \(\displaystyle 2924\)


\(\displaystyle \map s {2924}\) \(=\) \(\displaystyle \map \sigma {2924} - 2924\)
\(\displaystyle \) \(=\) \(\displaystyle 5544 - 2924\) $\sigma$ of $2924$
\(\displaystyle \) \(=\) \(\displaystyle 2620\)

$\blacksquare$


Sources