# A different type of converging sum

Calculus Level 5

$\large \sum_{p \ \in \ P - \{1\} } p^{-1}$

Let $$P$$ be the set of perfect powers. Evaluate the sum above to 2 decimal places. If you arrive at the conclusion that the sum diverges, enter your answer as 0.

Details:

• A positive integer $$n$$ is a perfect power if it can be represented as $$m^k$$ for some integers $$m > 0, k > 1$$.
• If a positive integer can be represented in multiple such ways, it still contributes to the sum only once.