International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 383-386

Tau numbers, natural density, and Hardy and Wright's theorem 437

Robert E. Kennedy and Curtis N. Cooper

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

Received 7 February 1989; Revised 9 March 1989

Copyright © 1990 Robert E. Kennedy and Curtis N. Cooper. 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.


An element of the set T= {n:τ(n) is a factor of n} is called a Tau number, where τ(n) denotes the number of divisors of the integer n. We determine the natural density of this set by use of Hardy and Wright's Theorem 437 (4th ed.).