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A Problem of Erdős and Kátai

Published online by Cambridge University Press:  26 February 2010

R. R. Hall
R. R. Hall
Affiliation:
Department of Mathematics, University of York, England.
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Extract

In this paper I prove the following result:

Theorem. Let f(d) be a multiplicative function such that |f(d)| ≤ 1 and ∑{ l/p : p ε P} = ∞, where P denotes the set of primes p for which f{p) = −1, and let v(n) denote the number of distinct prime factors ofn. Then for almost all n,

where A is an arbitrary constant > 3/e.

Type
Research Article
Information
Mathematika , Volume 21 , Issue 1 , June 1974 , pp. 110 - 113
Copyright
Copyright © University College London 1974

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References

1.Erdős, P. and Kátai, I.. “Non complete sums of multiplicative functions”, Periodica MathematicaHungarica, 1 (1971), 209–212.CrossRefGoogle Scholar
2.Erdős., P. “On some applications of probability to analysis and number theory”, J. LondonMath. Soc, 39 (1964), 692–696.CrossRefGoogle Scholar
3.Turán, P.. “On a theorem of Hardy and Ramanujan”, J. London Math. Soc, 9 (1934), 274–276.CrossRefGoogle Scholar
4.Hardy, G. H. and Ramanujan, S.. “The normal number of prime factors of a number n”, Quarterly J. of Math., 48 (1917), 76–92.Google Scholar