On a Sum Involving the Sum-of-Divisors Function - Feng Zhao; Jie Wu (Journal of Mathematics)
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.