A superior highly composite number is an integer where the ratio of its count of divisors to some power of the number is as high as possible. Expressing this as a formula:

Let d(n) be the number of divisors of n, including the number itself. For a given integer n, if there exists a number e such that d(n)/n^e is greater than or equal to d(k)/k^e for every integer k, then n is a highly composite number.

For more, see Superior highly composite number at Wikipedia, or A002201 at OEIS.

Here are the initial values:

2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800, 13967553600, 321253732800, 2248776129600, 65214507758400, 195643523275200, 6064949221531200

Your challenge is to take an index n, and output the nth number in this sequence.

You may use 0 or 1 indexing, and you may make a program which is only correct up to the limits of your language's data type(s), as long as it can handle the first 10 values at a minimum.

This is code golf. Standard loopholes apply.