Amicable Pair/Examples/2620-2924

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:

 $\ds \map s {2620}$ $=$ $\ds \map \sigma {2620} - 2620$ $\ds$ $=$ $\ds 5544 - 2620$ $\sigma$ of $2620$ $\ds$ $=$ $\ds 2924$

 $\ds \map s {2924}$ $=$ $\ds \map \sigma {2924} - 2924$ $\ds$ $=$ $\ds 5544 - 2924$ $\sigma$ of $2924$ $\ds$ $=$ $\ds 2620$

$\blacksquare$