Definition:Amicable Triplet/Definition 1
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Definition
Let $m_1, m_2, m_3 \in \Z_{>0}$ be (strictly) positive integers.
$\tuple {m_1, m_2, m_3}$ are an amicable triplet if and only if the aliquot sum of any one of them equals the sum of the other two:
- the aliquot sum of $m_1$ is equal to $m_2 + m_3$
and:
- the aliquot sum of $m_2$ is equal to $m_1 + m_3$
and:
- the aliquot sum of $m_3$ is equal to $m_1 + m_2$
Examples
$1980$, $2016$ and $2556$
- $\tuple {1980, 2016, 2556}$ form an amicable triplet.
$103 \, 340 \, 640$, $123 \, 228 \, 768$ and $124 \, 015 \, 008$
The following numbers form an amicable triplet:
- $103 \, 340 \, 640$
- $123 \, 228 \, 768$
- $124 \, 015 \, 008$
Also see
- Equivalence of Definitions of Amicable Triplet
- Results about amicable triplets can be found here.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $220$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $220$
- Weisstein, Eric W. "Amicable Triple." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AmicableTriple.html