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On the Sieve of Eratosthenes

Published online by Cambridge University Press:  20 November 2018

M. Ram Murty  and
S. Saradha
M. Ram Murty
Affiliation:
McGill University, Montréal, Québec
S. Saradha
Affiliation:
Concordia University, Montréal, Québec
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Let v(n) denote the number of distinct prime factors of a natural number n. A classical theorem of Hardy and Ramanujan states that the normal order of v(n) is log log n. That is, given any , the number of natural numbers not exceeding x which fail to satisfy the inequality

1

is o(x) as x → ∞. A very simple proof of this was subsequently given by Turán. He showed that

2

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 5 , 01 October 1987 , pp. 1107 - 1122
Copyright
Copyright © Canadian Mathematical Society 1987

References

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