On a Sum Involving the Sum-of-Divisors Function

Feng Zhao (1) , Jie Wu (2)

1 NCWU - North China University of Water Resources and Electric Power
2 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

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).

Domaines: Théorie des nombres [math.NT]

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