Definition:Amicable Pair/Definition 2

Definition
Let $m \in \Z_{>0}$ and $n \in \Z_{>0}$ be (strictly) positive integers. $m$ and $n$ are amicable numbers :
 * $\sigma \left({m}\right) = \sigma \left({n}\right) = m + n$

where $\sigma \left({m}\right)$ denotes the $\sigma$ function.

Also see

 * Equivalence of Definitions of Amicable Numbers