Distribution of Semi-k-Free Integers

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1973Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 37, page 340 (issn: 0002-9939,

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Authors: Suryanarayana, D.; Rao, R. Sita Rama Chandra;

doi: 10.2307/2039434 , 10.1090/s0002-9939-1973-0311599-1

Distribution of Semi-k-Free Integers

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Abstract

Let Qt(x) denote the number of semi-£-free integers £ix. It is known that Q*(x)=ai*x+0(x1/k), where a* is a constant. In this paper we prove that Aito = fiito - «I* = 0(x1/k cxp{-A lof^xQoglogx)-1^}), where A is an absolute positive constant. Further, on the assump- tion of the Riemann hypothesis, we prove that A*(x) = 0(jc2""+1> exp{/l log x(iog log x)~1}).

Keywords

Distribution of primes

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