The Oddness Function

Algebra Level pending

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 $$O(n)$$?

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