A remark on the means of the number of divisors

Document Type: Research Paper


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


‎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 $\frac{A_n}{G_n}$.


Main Subjects

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Volume 42, Issue 6
November and December 2016
Pages 1315-1330
  • Receive Date: 14 April 2015
  • Revise Date: 23 August 2015
  • Accept Date: 23 August 2015