Amicable Pair/Examples/2620-2924
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Example of Amicable Pair
$2620$ and $2924$ are the $3$rd amicable pair:
- $\map {\sigma_1} {2620} = \map {\sigma_1} {2924} = 5544 = 2620 + 2924$
Proof
Let $\map s n$ denote the aliquot sum of $n$.
By definition:
- $\map s n = \map {\sigma_1} n - n$
where $\map {\sigma_1} n$ denotes the divisor sum function.
Thus:
\(\ds \map s {2620}\) | \(=\) | \(\ds \map {\sigma_1} {2620} - 2620\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 5544 - 2620\) | $\sigma_1$ of $2620$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 2924\) |
\(\ds \map s {2924}\) | \(=\) | \(\ds \map {\sigma_1} {2924} - 2924\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 5544 - 2924\) | $\sigma_1$ of $2924$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 2620\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2620$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2620$
- Weisstein, Eric W. "Amicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicablePair.html