A generalization of a theorem by Cheo and Yien concerning digital sums
For a non-negative integer n, let s(n) denote the digital sum of n. \textit{P. Cheo} and \textit{S. Yien} [Acta Math. Sin. 5, 433-438 (1955; Zbl 0068.266)] proved that for a positive integer x, the sum of the terms of the sequence \(\{\) s(n): \(n=0,1,2,...,(x-1)\}\) is (4.5)x log x\(+O(x)\). In this paper we let k be a positive integer and determine that the sum of the sequence \(\{\) s(kn): \(n=0,1,2,...,(x-1)\}\) is also (4.5)x log x\(+O(x)\) where the constant depends on k.
scientific article; zbMATH DE number 3975032