A remark on the means of the number of divisors

Hassani, M.

A remark on the means of the number of divisors

Document Type : Research Paper

Author

M. Hassani

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

Abstract

‎We obtain the asymptotic expansion of the sequence with general term $\frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $\d(1),\d(2),\dots,\d(n)$‎, ‎with $\d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $\frac{A_n}{G_n}$.

Keywords

Main Subjects

11-XX Number theory

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