Document Type: Research Paper

Author

Department of Mathematics, University of Zanjan University Blvd., 45371-38791, Zanjan.

Abstract

The asymptotic behaviour of the sequence with general term $P_n=(\varphi(1)+\varphi(2)+\cdots+\varphi(n))/(1+2+\cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $P_n-6/\pi^2$ is found.

Keywords

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[3] E. Landau, Sur les valeurs moyennes de certaines fonctions arithmétiques, Bull. Acad. Royale Belgique, (1911) 443--472.

[4] G. Tenenbaum, Introduction to analytic and probabilistic number theory, Cambridge Studies in Advanced Mathematics 46, Cambridge University Press, Cambridge, 1995.

[5] A. Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Mathematische Forschungsberichte, XV. VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.