Amicable Pair/Examples/5020-5564

Example of Amicable Pair

$5020$ and $5564$ are the $4$th amicable pair:

$\map {\sigma_1} {5020} = \map {\sigma_1} {5564} = 10 \, 584 = 5020 + 5564$

Proof

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

By definition:

$\map s n = \map {\sigma_1} n - n$

where $\sigma_1$ denotes the divisor sum function.

Thus:

\(\ds \map s {5020}\)

\(=\)

\(\ds \map {\sigma_1} {5020} - 5020\)

\(\ds \)

\(=\)

\(\ds 10 \, 584 - 5020\)

$\sigma_1$ of $5020$

\(\ds \)

\(=\)

\(\ds 5564\)

\(\ds \map s {5564}\)

\(=\)

\(\ds \map {\sigma_1} {5564} - 5564\)

\(\ds \)

\(=\)

\(\ds 5544 - 5564\)

$\sigma_1$ of $5564$

\(\ds \)

\(=\)

\(\ds 10 \, 584\)

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5020$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5020$

• Weisstein, Eric W. "Amicable Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicablePair.html