How many Lynch-Bell numbers are there? Challenge

Given an integer, n, as input where 36 &gt;= n &gt;= 2, output how many Lynch-Bell numbers there are in base n.

The output must be in base 10.

Lynch-Bell Numbers

A number is a Lynch-Bell numbers if:


All of its digits are unique (no repetition of digits)
The number is divisible by each of its digits
It doesn't contain zero as one of its digits


Since, all of the digits have to be unique, and you have a finite set of single digit numbers in each base, there is a finite number of Lynch-Bell numbers.

For example, in base 2 there is only one Lynch-Bell number, 1, since all other numbers either repeat digits or contain a 0.

Examples

Input &gt; Output
2 &gt; 1
3 &gt; 2
4 &gt; 6
5 &gt; 10
6 &gt; 10
7 &gt; 75
8 &gt; 144
9 &gt; 487
10 &gt; 548


Mathematica Online ran out of memory above base 10. You can use the following code to generate your own:

Do[Print[i," &gt; ",Count[Join@@Permutations/@Rest@Subsets@Range[#-1],x_/;And@@(x\[Divides]FromDigits[x,#])]&amp;[i]],{i,10,36,1}]


Winning

Shortest code in bytes wins.
Jelly, 13 bytes

Q⁼g
*`Ṗ©bç"®S


Try it online!

Another O(nn) solution.

Explanation

Q⁼g  Helper link. Input: digits (LHS), integer (RHS)
Q    Unique (digits)
 ⁼   Match
  g  GCD between each digit and the integer

*`Ṗ©bç"®S  Main link. Input: integer n
*`         Compute n^n
  Ṗ        Pop, forms the range [1, n^n-1]
   ©       Store previous result in register
    b      Convert each integer to base n
     ç"    Call the helper link, vectorized, with
       ®   The register's value
        S  Sum