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On a Sum Involving the Sum-of-Divisors Function

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  • Feng Zhao
  • Jie Wu
  • Tianping Zhang

Abstract

Let σn be the sum of all divisors of n and let t be the integral part of t. In this paper, we shall prove that ∑n≤xσx/n=π2/6x  log  x+Oxlog  x2/3log2  x4/3 for x⟶∞, and that the error term of this asymptotic formula is Ωx.

Suggested Citation

  • Feng Zhao & Jie Wu & Tianping Zhang, 2021. "On a Sum Involving the Sum-of-Divisors Function," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, April.
    • Handle: RePEc:hin:jjmath:5574465
    DOI: 10.1155/2021/5574465
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