Java 8, 151 111 110 101 98 bytes

n->{int r=0,x=10000,i;for(;x-->0;r-=i-n>>-1)for(i=x;i-->1&&(x<i*i|x%i>0||(i=x/i-i)>i););return r;}

-10 bytes thanks to @Nevay.
-3 bytes thanks to @ceilingcat.

Explanation:

Try it here.

n->{                  // Method with integer as parameter and return-type
  int r=0,            //  Result-integer, starting at 0
      x=10000,        //  Index-integer `x` for the outer loop, starting at 10,000
      i;              //  Index-integer `i` for the inner loop, uninitialized
  for(;x-->0;         //  Loop `x` in the range (10000, 0]:
      r-=i-n>>-1)     //   If the MaxMin-Divisor Pair's difference is lower than the input,
                      //    add 1 to the result (after every iteration)
    for(i=x;i-->1     //   Inner loop `i` in the range (`x`, 1]:
        &&(x<i*i      //    If the current square of `i` is smaller than or equals to `x`,
           |x%i>0     //    and the current `x` is divisible by `i`:
           ||(i=x/i-i)//     Calculate the MaxMin-Division difference
             >i););   //     And stop the inner loop
  return r;}          //  After the loops, return the result