Definition:Amicable Pair

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

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

Many sources refer to the elements of an amicable pair as amicable numbers. While this usage is common and widespread, it is preferred not to be used on in order that the distinction is clear between amicable pairs, amicable triplets and so on.

Also see

 * The obligatory XKCD link: https://xkcd.com/410/


 * Equivalence of Definitions of Amicable Pair


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


 * Definition:Amicable Triplet