Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a conjecture of Kátai concerning weakly composite numbers


Author: Janos Galambos
Journal: Proc. Amer. Math. Soc. 96 (1986), 215-216
MSC: Primary 11A25; Secondary 11N37
MathSciNet review: 818446
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A number is called weakly composite if the sum of the reciprocals of its prime divisors is bounded by two. In this note it is proved that, for $ n \geqslant {n_0}$, there is a weakly composite number between $ n$ and $ n + \log \log \log n$.


References [Enhancements On Off] (What's this?)

  • [1] P. D. T. A. Elliott, Probabilistic number theory. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 239, Springer-Verlag, New York-Berlin, 1979. Mean-value theorems. MR 551361
  • [2] Miriam Hausman, Generalization of a theorem of Landau, Pacific J. Math. 84 (1979), no. 1, 91–95. MR 559630
  • [3] I. Kátai, A minimax theorem for additive functions, Publ. Math. Debrecen 30 (1983), no. 3-4, 249–252 (1984). MR 739486

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11A25, 11N37

Retrieve articles in all journals with MSC: 11A25, 11N37


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0818446-9
Article copyright: © Copyright 1986 American Mathematical Society