\[ g(n)= \begin{cases} 1, \quad \quad\quad \quad\quad\quad\quad\quad\quad \quad n = 2^0, 2^1, 2^1, 2^2, \ldots \\ \displaystyle \prod_{\text{odd prime }p} \left( \dfrac{p-1}2 \right)^{v_p (n) }, \quad \text{otherwise} \end{cases} \]

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