Amicable Triplet/Examples/1980-2016-2556

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