\begin{definition}[Definition:Amicable Pair/Definition 2]
Let $m \in \Z_{>0}$ and $n \in \Z_{>0}$ be (strictly) positive integers.
$m$ and $n$ are an '''amicable pair''' {{iff}}:
:$\map {\sigma_1} m = \map {\sigma_1} n = m + n$
where $\sigma_1$ denotes the divisor sum function.
\end{definition}