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Asymptotic Formulae for
the $n$-th Perfect Power Rafael Jakimczuk
División Matemática
Universidad Nacional de Luján
Buenos Aires
Argentina
mailto:jakimczu@mail.unlu.edu.arjakimczu@mail.unlu.edu.ar

In memory of my sister Fedra Marina Jakimczuk (1970-2010)

Abstract:

Let $P_n$ be the $n$-th perfect power. In this article we prove asymptotic formulae for $P_n$. For example, we prove the following formula

$$P_n=n^2-2n^{5/3}-2 n^{7/5} +\frac{13}{3}n^{4/3}-2n^{9/7}+2n^{6/5}-2n^{13/11}+o\left(n^{13/11}\right).$$