On a conjecture of Kátai concerning weakly composite numbers
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- by Janos Galambos PDF
- Proc. Amer. Math. Soc. 96 (1986), 215-216 Request permission
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
- P. D. T. A. Elliott, Probabilistic number theory. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 239, Springer-Verlag, New York-Berlin, 1979. Mean-value theorems. MR 551361, DOI 10.1007/978-1-4612-9989-9
- Miriam Hausman, Generalization of a theorem of Landau, Pacific J. Math. 84 (1979), no. 1, 91–95. MR 559630, DOI 10.2140/pjm.1979.84.91
- I. Kátai, A minimax theorem for additive functions, Publ. Math. Debrecen 30 (1983), no. 3-4, 249–252 (1984). MR 739486
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 215-216
- MSC: Primary 11A25; Secondary 11N37
- DOI: https://doi.org/10.1090/S0002-9939-1986-0818446-9
- MathSciNet review: 818446