Definition:Amicable Pair/Definition 2

Definition
Let $m \in \Z_{>0}$ and $n \in \Z_{>0}$ be (strictly) positive integers. $m$ and $n$ are an amicable pair :
 * $\map {\sigma_1} m = \map {\sigma_1} n = m + n$

where $\sigma_1$ denotes the divisor sum function.

Also see

 * Equivalence of Definitions of Amicable Pair