Amicable Triplet/Examples/1980-2016-2556
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Example of Amicable Triplet
- $\tuple {1980, 2016, 2556}$ form an amicable triplet.
Proof
We have
\(\ds \map {\sigma_1} {1980}\) | \(=\) | \(\ds 6552\) | $\sigma_1$ of $1980$ | |||||||||||
\(\ds \map {\sigma_1} {2016}\) | \(=\) | \(\ds 6552\) | $\sigma_1$ of $2016$ | |||||||||||
\(\ds \map {\sigma_1} {2556}\) | \(=\) | \(\ds 6552\) | $\sigma_1$ of $2556$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 1980 + 2016 + 2556\) |
Hence the result, by definition of amicable triplet.
$\blacksquare$
Sources
- 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1980$
- Weisstein, Eric W. "Amicable Triple." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicableTriple.html