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On a Sum Involving the Sum-of-Divisors Function

Abstract : Let σ(n) be the sum of all divisors of n and let [t] be the integral part of t. In this paper, we shall prove that Σn≤x σ([x/n]) = (π 2 /6)x log x + O(x(log x) (2/3) (log 2 x) (4/3)) for x ⟶ ∞, and that the error term of this asymptotic formula is Ω(x).
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https://hal.archives-ouvertes.fr/hal-03305600
Contributor : Jie Wu <>
Submitted on : Wednesday, July 28, 2021 - 6:23:14 PM
Last modification on : Thursday, July 29, 2021 - 3:35:48 AM

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Feng Zhao, Jie Wu. On a Sum Involving the Sum-of-Divisors Function. Journal of Mathematics, Hindawi, 2021, 2021, pp.5574465. ⟨10.1155/2021/5574465⟩. ⟨hal-03305600⟩

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