Definition:Amicable Triplet/Definition 2

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 :
 * $\map {\sigma_1} {m_1} = \map {\sigma_1} {m_2} = \map {\sigma_1} {m_3} = m_1 + m_2 + m_3$

where $\sigma_1$ denotes the divisor sum function.

Also see

 * Equivalence of Definitions of Amicable Triplet