International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 495-499
doi:10.1155/S0161171202007615
Graceful numbers
Department of Mathematics, The Catholic University of America, Washington, DC 20064, USA
Received 14 May 2001
Copyright © 2002 Kiran R. Bhutani and Alexander B. Levin. 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.
Abstract
We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. As a consequence, we determine which graceful numbers are perfect.