This article is cited in 4 papers

On the Quantity of Numbers of Special Form Depending on the Parity of the Number of Their Different Prime Divisors

M. E. Changa

Moscow State University of Geodesy and Cartography

Abstract: Natural numbers all of whose prime divisors (even or odd in number) belong to special sets are considered. It is proved that numbers with an odd number of different prime divisors predominate; more precisely, the difference between these numbers not exceeding a given $x$ tends to infinity with increasing $x$.

Keywords: natural number, prime divisor, Euler's identity, Dirichlet generating series, Perron's formula, Cauchy's integral theorem.

UDC: 511

Received: 02.10.2014

DOI: 10.4213/mzm10658

 English version: Mathematical Notes, 2015, 97:6, 941–945

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