De Koninck, Jean-Marie (ed.) et al., Anatomy of integers. Based on the CRM workshop, Montreal, Canada, March 13–17, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4406-9/pbk). CRM Proceedings and Lecture Notes 46, 167-173 (2008).
Let denote the sum of divisors function. The authors call an integer a Descartes number if is odd and if for two integers such that
Theorem 1. If is a cube-free Descartes number which is not divisible by 3, then for some odd almost perfect number , and has more than one million distinct prime divisors.
Theorem 2. The number is the only cube-free Descartes number with fewer than seven distinct prime divisors.
|11A25||Arithmetic functions, etc.|
|11N25||Distribution of integers with specified multiplicative constraints|