Primitive weird numbers having more than three distinct prime factors

Amato, Gianluca (Universita G. D'Annunzio di Chieti-Pescara Dipartimento di Economia) ; Hasler, Maximilien (Université des Antilles, Département Scientifique Interfacultaire) ; Melfi, Giuseppe (Haute école de gestion Arc, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale) ; Parton, Maurizio (Universita G. D'Annunzio di Chieti-Pescara Dipartimento di Economia)

In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield pri- mitive weird numbers of the form mp1 ... pk for a suitable deficient positive integer m and primes p1 , ... , pk and generalize a recent technique developed for generating primitive weird numbers of the form 2n p1 p2 . The same techniques can be used to search for odd weird numbers, whose existence is still an open question.


Mots-clés:
Type d'article:
scientifique
Faculté:
Economie et Services
Ecole:
HEG Arc
Institut:
Institut du Management et des Systèmes d'Information
Classification:
Economie/gestion
Date:
2016
Publié dans
Rivista di matematica della Università di Parma : proceeding of the Third Italian Number Theory Meeting, Pisa (Italy), 21-24 September 2015
Numérotation (vol. no.):
2016, vol. 7, no. 1, pp. 153-163
ISSN:
0035-6298
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 Notice créée le 2016-10-17, modifiée le 2018-12-05

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