\begin{definition}[Definition:Amicable Triplet/Definition 1]
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''' {{iff}} 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 $m_1 + m_2$
\end{definition}