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

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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 , there is a weakly composite number between and .

**[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**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0818446-9

Article copyright:
© Copyright 1986
American Mathematical Society