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 :
 * $\map \sigma m = \map \sigma n = m + n$

where $\map \sigma m$ denotes the $\sigma$ function.

Also see

 * Equivalence of Definitions of Amicable Pair