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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