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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