Definition:Amicable Triplet/Definition 1

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 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 $m_1 + m_2$

Also see

 * Equivalence of Definitions of Amicable Triplet