On a sum involving the sum-of-divisors function
Summary: Let \(\sigma (n)\) be the sum of all divisors of \(n\) and let \([t]\) be the integral part of \(t\). In this paper, we shall prove that \(\sum_{n \leq x} \sigma ([x/n]) = (\pi^2/6)x\log x+O (x(\log x)^{(2/3)} (\log_2 x)^{(4/3)})\) for \(x\longrightarrow\infty\), and that the error term of this asymptotic formula is \(\Omega (x)\).
scientific article; zbMATH DE number 7363424