Geodesic
On the Quantity of Numbers of Special Form Depending on the Parity of the Number of Their Different Prime Divisors
Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 930-935 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, Cauchy's integral theorem.
Mots-clés : Perron's formula 
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M. E. Changa. On the Quantity of Numbers of Special Form Depending on the Parity of the Number of Their Different Prime Divisors. Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 930-935. http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a10/

[1] I. M. Vinogradov, “Nekotoroe obschee svoistvo raspredeleniya prostykh chisel”, Matem. sb., 7:2 (1940), 365–372 | MR | Zbl

[2] M. E. Changa, “Prostye chisla v spetsialnykh promezhutkakh i additivnye zadachi s takimi chislami”, Matem. zametki, 73:3 (2003), 423–436 | DOI | MR | Zbl

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

[4] A. A. Karatsuba, “Ob odnom svoistve mnozhestva prostykh chisel”, UMN, 66:2 (2011), 3–14 | DOI | MR | Zbl

[5] A. A. Karatsuba, “Ob odnom svoistve mnozhestva prostykh chisel kak multiplikativnogo bazisa naturalnogo ryada”, Dokl. RAN, 439:2 (2011), 159–162 | MR | Zbl

[6] M. E. Changa, “O chislakh, vse prostye deliteli kotorykh lezhat v spetsialnykh promezhutkakh”, Izv. RAN. Ser. matem., 67:4 (2003), 213–224 | DOI | MR | Zbl

[7] M. E. Changa, Metody analiticheskoi teorii chisel, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.-Izhevsk, 2013