Amicable Pair/Examples/2620-2924

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