Count the Common Factors - A possible new problem

Clive, thank you very much!

The problem is live now

And it seems to be of that kind of "magical" arithmetic sequences of operations which fascinated me from childhood and in which I was nevertheless always poor :) Going to try it now...

sincerely yours, Rodion

Well, seems I have it done, but I really feel miserable :)

First of all I haven't come up with precise proof of my approach (which probably is correct, just need to be proved). Secondly, I probably spent 40 minutes on fixing my factors counting loop. I guess this task should be added to chain of simple ones, a kind of fine "advanced simple" really :)