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Hostile Divisor Numbers

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)

Examples

Number 9566 has 4 divisors: 1, 2, 4783 and 9566
(as you can see, no two of them share the same digit).
Thus, 9566 is a Hostile Divisor Number

Number 9567 is NOT HDN because its divisors (1, 3, 9, 1063, 3189, 9567) share some common digits.

Here are the first few HDN

1,2,3,4,5,6,7,8,9,23,27,29,37,43,47,49,53,59,67,73,79,83,86,87,89,97,223,227,229,233,239,257,263,267,269,277,283,293,307,337...

Task

The above list goes on and your task is to find the nth HDN

Input

A positive integer n from 1 to 4000

Output

The nth HDN

Test Cases

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.

EDIT

Good news! I submitted my sequence to OEIS and...
Hostile Divisor Numbers are now OEIS A307636

Answer*

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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Edit Summary*

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\$\begingroup\$ Can you please add a TIO link so that everybody can check your answer? \$\endgroup\$

ZaMoC
– ZaMoC

2019年05月03日 16:40:07 +00:00
Commented May 3, 2019 at 16:40
\$\begingroup\$ 95 bytes: (n=t=1;While[t<=#,If[!Or@@IntersectingQ@@@Subsets[IntegerDigits@Divisors@n,{2}],t++];n++];n-1)& I am not planning to post an answer so I will leave this here \$\endgroup\$

ZaMoC
– ZaMoC

2019年05月03日 16:45:18 +00:00
Commented May 3, 2019 at 16:45
\$\begingroup\$ @J42161217, I've been trying to get the code to work in TIO without success. There must be some trick I'm missing. \$\endgroup\$

DavidC
– DavidC

2019年05月03日 20:55:39 +00:00
Commented May 3, 2019 at 20:55
\$\begingroup\$ @J42161217, Your code seems to work but takes 3 times the runtime. You can submit it as your own. (Maybe I'll learn how to implement TIO from your example.) \$\endgroup\$

DavidC
– DavidC

2019年05月03日 20:57:07 +00:00
Commented May 3, 2019 at 20:57
1

\$\begingroup\$ 72 bytes using For instead of While, E!=##& to test for repeated digits \$\endgroup\$

att
– att

2019年05月03日 22:23:04 +00:00
Commented May 3, 2019 at 22:23

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