The Oddness Function

For any integer $n \geq 3$ , we define $O(n)$ to be "the oddness of n", which is the product of all the (not necessarily unique) odd prime factors of $n$ .

For example, since $300 = 2^2 \times 3 \times 5^2$ , so $O(300) = 1 \times 3 \times 5^2$ .

What is the smallest possible value of $O(n)$ ?