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On sparsely totient numbers

Published online by Cambridge University Press:  18 May 2009

Glyn Harman
Glyn Harman
Affiliation:
School of Mathematics, University of Wales, College of Cardiff, Senghenydd Road, Cardiff CF2 4AG.
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Following Masser and Shiu [6] we say that a positive integer n is sparsely totient if

Here φ is the familiar Euler totient function. We write ℱ for the set of sparsely totient numbers. In [6] several results are proved about the multiplicative structure of ℱ. If we write P(n) for the largest prime factor of n then it was shown (Theorem 2 of [6]) that

and infinitely often

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991 , pp. 350 - 358
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Baker, R. C., Diophantine inequalities, London Math. Soc. Monographs N.S.I (Oxford Science Publications, 1986).Google Scholar
2.Baker, R. C., The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193–231.CrossRefGoogle Scholar
3.Baker, R. C. and Harman, G., On the distribution of apkmodulo one, Mathematika, to appear.Google Scholar
4.Davenport, H., Multiplicative number theory, second edition revised by Montgomery, H. L. (Springer, 1980).Google Scholar
5.Heath-Brown, D. R., Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365–1377.Google Scholar
6.Masser, D. W. and Shiu, P., On sparsely totient numbers, Pacific J. Math. 121 (1986), 407–426.Google Scholar
7.Titchmarsh, E. C., The theory of the Riemann zeta-function, second edition revised by Heath-Brown, D. R. (Oxford, 1986).Google Scholar