Amicable pairs were discovered or known already by Pythagoreans. There are several formulas to calculate Amicable pairs discovered from around 860 by Thābit ibn Qurra and further researched by Amicable Eastern and Western matematicians.
There is no universal function or formula to describe them all. But there is a project on BOINC to compute these numbers. There are around 1.2 milliards pairs discovered by now; kept in a database for a futher research by matematicians.
Around 450 new pairs was discovered on my laptop with BOINC Amicable pairs project so far.
Unfortunately, this project is not running on a mobile phone as it is requring a lot of resources. It can be run on a laptop and better on GPU.
Good news = if you like to join this Amicable effort, it is enough to join for a week with a powerful PC and discover one or more new Amicable pairs.
More good news = Amicable pair is a Gridcoin project that earns GRC either by solo mining or with a GRC pool. There is always a way to donate these coins if it is not an intention to earn with this project. Gridcoin blockchain is good to developing crowd science and maybe worth participation too.