I need to find all decimal numbers $a1,a2,a3,...,an$ in a range [0; $10^15$] which have following property: digit sum of $a1$ equals digit sum of $x*a1$ for any decimal number $x>0$.

I found this link http://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?