International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 537-543

On an asymptotic formula for the niven numbers

Curtis N. Cooper and Robert E. Kennedy

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

Received 20 May 1985

Copyright © 1985 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.


A Niven number is a positive integer which is divisible by its digital sum. A discussion of the possibility of an asymptotic formula for N(x) is given. Here, N(x) denotes the nmber of Niven numbers less than x. A partial result will be presented. This result will be an asymptotic formula for Nk(x) which denotes the number of Niven numbers less than x with digital sum k.