Weird series!

Number Theory Level pending

Let \(\mathbb{A}\) be the set of all the numbers that an be expressed as \(a^{b}\), for \(a, b>1\) and \(a, b\in\mathbb{Z}\). What is the value of \(\sum_{k\in\mathbb{A}} \frac{1}{k-1}\)?

Enter 0 if you think the series diverges.

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