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On the conditional infiniteness of primitive weird numbers.
- Source :
-
Journal of Number Theory . Feb2015, Vol. 147, p508-514. 7p. - Publication Year :
- 2015
-
Abstract
- Text A weird number is a number n for which σ ( n ) > 2 n and such that n is not a sum of distinct proper divisors of n . In this paper we prove that n = 2 k p q is weird for a quite large set of primes p and q . In particular this gives an algorithm to generate very large primitive weird numbers, i.e., weird numbers that are not multiple of other weird numbers. Assuming classical conjectures on the gaps between consecutive primes, this also would prove that there are infinitely many primitive weird numbers, a question raised by Benkoski and Erdős in 1974. Video For a video summary of this paper, please visit http://youtu.be/OS93l3a_Mjo . [ABSTRACT FROM AUTHOR]
- Subjects :
- *NUMBER theory
*PROOF theory
*ALGORITHMS
*SMALL divisors
*MATHEMATICAL functions
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 147
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 99405766
- Full Text :
- https://doi.org/10.1016/j.jnt.2014.07.024