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Matematicheskie Zametki, 2015, Volume 97, Issue 6, Pages 930–935
DOI: https://doi.org/10.4213/mzm10658 (Mi mzm10658) 		 
This article is cited in 4 scientific papers (total 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
Full-text PDF (385 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm10658
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.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation (grant no. 14-11-00433 “Combinatorial, geometric, and analytic problems of number theory”).
Received: 02.10.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 6, Pages 941–945
DOI: https://doi.org/10.1134/S0001434615050296
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: M. E. Changa, “On the Quantity of Numbers of Special Form Depending on the Parity of the Number of Their Different Prime Divisors”, Mat. Zametki, 97:6 (2015), 930–935; Math. Notes, 97:6 (2015), 941–945
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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