Astonishing result

Calculus Level 4

\[ \sum_{i=1}^{\infty} \sum_{j=1}^{\infty} \sum_{k=1}^{\infty} \dfrac{1}{(ijk)^2} = \dfrac{\pi^a}{b},\]

where \(a\) and \(b\) are integers. Find \(\frac{b}{a}.\)

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