International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 817-820

A generalization of a theorem by Cheo and Yien concerning digital sums

Curtis N. Cooper and Robert E. Kennedy

Department of Mathematics and Computer Science, Central Missouri State University, Warrensburg 64093, Missouri, USA

Received 20 January 1986

Copyright © 1986 Curtis N. Cooper and Robert E. Kennedy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a non-negative integer n, let s(n) denote the digital sum of n. Cheo and Yien proved that for a positive integer x, the sum of the terms of the sequence{s(n):n=0,1,2,,(x1)}is (4.5)xlogx+0(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,,(x1)}is also (4.5)xlogx+0(x). The constant implicit in the big-oh notation is dependent on k.