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The equation ω(n) = ω(n + 1)

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

J.-C. Schlage-Puchta
J.-C. Schlage-Puchta
Affiliation:
Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstr. 1. 79111 Freiburg, Germany.
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Abstract

It is proved that there are infinitely many integers n such that n and n + 1 have the same number of distinct prime divisors.

MSC classification

Secondary: 11N37: Asymptotic results on arithmetic functions

Information

Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 99 - 101
Copyright
Copyright © University College London 2003

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References

1.Heath-Brown, D. R.. Almost-prime k-tuples, Mathematika 44 (1997), 245–266.CrossRefGoogle Scholar
2.Heath-Brown, D. R.. The divisor function at consecutive integers, Mathematika 31 (1984), 141–149.CrossRefGoogle Scholar