Kata

You have a natural number d.

You need to write a function f(d) which finds the smallest positive number n having d divisors .

For example:

f(1) = 1
f(3) = 4
f(60) = 5040
f(420) = 9979200

In this kata all the tests will be with 1 <= d <= 10000

Keep in mind that n can be on the order of $10^{300}10^\{300\}$, so iterating over n and finding the divisors in total for $O(n\sqrt{\phantom{(}n})O(n\backslash sqrt\{\backslash mathstrut\; n\})$ operations is not an option.

Good luck!