Definition:Amicable Pair

Definition
Let $m \in \Z_{>0}$ and $n \in \Z_{>0}$ be (strictly) positive integers.

$m$ and $n$ are amicable numbers they form a sociable chain of order $2$.

That is:
 * the aliquot sum of $m$ is equal to $n$

and:
 * the aliquot sum of $n$ is equal to $m$.

Also known as
Amicable numbers are often referred to as amicable pairs, which acknowledges the fact that they come in sets of $2$ at a time.

Some sources refer to them as friendly pairs, but this is deprecated as the term friendly pair is usually used for something different.

Also see

 * Definition:Sociable Number
 * Definition:Sociable Chain
 * Definition:Quasiamicable Numbers