On the Sieve of Eratosthenes

M. Ram Murty, S. Saradha

Type: Article

Publication Date: 1987-10-01

Citations: 9

DOI: https://doi.org/10.4153/cjm-1987-056-8

Abstract

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

Locations

Canadian Journal of Mathematics - View - PDF

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