Is there any efficient way to generate these numbers?
The sequence OEIS A038367: Numbers $n$ with property that (product of digits of $n$) is divisible by (sum of digits of $n$).
First few: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 22, 30, 36, 40, 44, 50, \ldots$
Suppose I want to generate $10^9$th such number. Is there any efficient mathematical theory/research paper to generate such a number.
Actually, I have to write a program to generate $10^9$ such numbers, and the execution time limit is only $20$ seconds. So the normal or simple way will take a month to produce the result, so their might be some complex or special efficient methods? Can you please help me in solving this mathematical problem?