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Sums of perfect powers. (English) Zbl 1285.11051
Summary: Let $$P_n$$ be the $$n$$th perfect power. In this article we obtain asymptotic formulae for the sum $$\sum_{i=1}^n P_i$$. We also prove the following formulae $\sum_{i=1}^n \frac 1{\sqrt{P_i}}=\log n+C+o(1),\quad \sum_{P_n\leq x} \frac 1{\sqrt{P_i}}=\frac 12 \log x+C+o(1),$ where $$C$$ is a constant.
##### MSC:
 11B83 Special sequences and polynomials 11N25 Distribution of integers with specified multiplicative constraints
##### Keywords:
perfect powers; sums of perfect powers
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