%0 Journal Article
%T Sums of perfect powers
%A R. Jakimczuk
%J International Journal of Contemporary Mathematical Sciences
%D 2013
%I 
%X Let $P_n$ be the $n$-th perfect power. In this article we obtain asymptotic formulae for the sum $sum^{n}_{i=1}P_i$. We also prove the following formulae[sum^{n}_{i=1}frac{1}{sqrt{P_i}}=log n+C+o(1),qquad sum_{P_nleq x}frac{1}{sqrt{P_n}}=frac{1}{2}log x+C+o(1),]where $C$ is a constant.
%K Perfect powers
%K sums of perfect powers
%U http://www.m-hikari.com/ijcms/ijcms-2013/1-4-2013/jakimczukIJCMS1-4-2013.pdf