#Java 8, 151 111 110 101 bytes
n->{int r=0,x=10000,i;for(;x-->0;r-=i-n>>-1)for(i=x;i-->1;)if(x>=i*i&x%i<1){i=x/i-i;break;}return r;}
-10 bytes thanks to @Nevay.
Explanation:
n->{ // Method with integer as parameter and return-type
int r=0, // Result-integer
x=10000, // Index-integer starting at 10,000
i; // Another index-integer for the inner loop
for(;x-->0; // Loop (1) from 10,000 down to 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, // Set `i` to `x`
i-->1;) // Inner loop (2) from `i` downwards to 1
if(x>=i*i // If the current square-root of `x` is smaller than or equal to `i`,
&x%i<1){ // and if the current `x` is divisible by `i`:
i=x/i-i; // Calculate the MaxMin-Division difference
break;} // And leave the inner loop (2)
// End of inner loop (2) (implicit / single-line body)
// End of loop (1) (implicit / single-line body)
return r; // Return the result
} // End of method