Infinite Products!

Calculus Level 3

For x>1x > 1, define f(x)=n=2(11nx)\displaystyle f(x) = \prod_{n=2}^{\infty} \left(1 - \dfrac{1}{n^x}\right).

Find the value of f(6)f2(3)\dfrac{f(6)}{f^2(3)}.

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