Some divisors of positive integers really hate each other and they don't like to share one or more common digits.
Those integers are called Hostile Divisor Numbers (HDN)
1, 2, 4783 and 9566
(as you can see, no two of them share the same digit).
Thus, 9566 is a Hostile Divisor Number
9567 is NOT HDN because its divisors (
1, 3, 9, 1063, 3189, 9567) share some common digits.
Here are the first few HDN
The above list goes on and your task is to find the nth HDN
A positive integer
here are some 1-indexed test cases.
Please state which indexing system you use in your answer to avoid confusion.
input -> output 1 1 10 23 101 853 1012 26053 3098 66686 4000 85009
This is code-golf, so the lowest score in bytes wins.
I submitted my sequence to OEIS and...
Hostile Divisor Numbers are now OEIS A307636