Ordinary problem

S=n=1σ4(n)n8 S = \displaystyle \sum_{n=1}^{\infty} \dfrac{\sigma_{4}(n)}{n^{8}}

Find π12S\dfrac{\pi^{12}}{S}.

Notation: σx(n)\sigma_x(n) denotes the sum of the xthx^\text{th} powers of the positive divisors of nn.

Hint: Use Bernoulli numbers to calculate the value of Riemann Zeta function. .

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