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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 495-499
doi:10.1155/S0161171202007615

Graceful numbers

Kiran R. Bhutani and Alexander B. Levin

Department of Mathematics, The Catholic University of America, Washington, DC 20064, USA

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.