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On the quantity of numbers of special form depending on the parity of the number of their different prime divisors

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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.

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References

  1. I. M. Vinogradov, “A general property of the distribution of prime numbers,” Mat. Sb. 7(2), 365–372 (1940).

    Google Scholar 

  2. M. E. Changa, “Prime numbers in special intervals and additive problems with such numbers,” Mat. Zametki 73(3), 423–436 (2003) [Math. Notes 73 (3–4), 389–401 (2003)].

    Article  MathSciNet  Google Scholar 

  3. C. Mauduit and J. Rivat, “Sur un problème de Gelfond: la somme des chiffres des nombres premiers,” Ann. of Math. (2) 171(3), 1591–1646 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. A. Karatsuba, “On a property of the set of prime numbers,” Uspekhi Mat. Nauk 66(2), 3–14 (2011) [RussianMath. Surveys 66 (2), 209–220 (2011)].

    Article  MathSciNet  Google Scholar 

  5. A. A. Karatsuba, “On a property of the set of primes as a multiplicative basis of natural numbers,” Dokl. Ross. Akad. Nauk Russian Academy of Sciences 439(2), 159–162 (2011) [Dokl. Math. 84 (1), 467–470 (2011)].

    Google Scholar 

  6. M. E. Changa, “On numbers all of whose prime divisors lie in special intervals,” Izv. Ross. Akad. Nauk Ser. Mat. 67(4), 213–224 (2003) [Izv.Math. 67 (4), 837–848 (2003)].

    Article  MathSciNet  Google Scholar 

  7. M. E. Changa, Methods of Analytic Number Theory (Nauchn.-Issled. Tsentr “Regular and Chaotic Dynamics,” Moscow-Izhevsk, 2013) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University of Geodesy and Cartography, Moscow, Russia

    M. E. Changa

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  1. M. E. Changa
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Correspondence to M. E. Changa.

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Original Russian Text © M. E. Changa, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 6, pp. 930–935.

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Changa, M.E. On the quantity of numbers of special form depending on the parity of the number of their different prime divisors. Math Notes 97, 941–945 (2015). https://doi.org/10.1134/S0001434615050296

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  • DOI: https://doi.org/10.1134/S0001434615050296

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