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I. Kàtai. Distribution of q-additive functions, in “Probability Theory and Applications” Kluwer Academic, Dordrecht, p. 309-318, (1992).

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Article

Sums over Numbers with Restricted Prime Factors

1Department of Mathematics, Faculty of Sciences of Monastir, Tunisia

2Faculté des sciences de Sfax, BP 1171, Sfax 3000, Tunisie


Turkish Journal of Analysis and Number Theory. 2017, Vol. 5 No. 5, 153-158
DOI: 10.12691/tjant-5-5-2
Copyright © 2017 Science and Education Publishing

Cite this paper:
Khadija Mbarki, Walid Wannes. Sums over Numbers with Restricted Prime Factors. Turkish Journal of Analysis and Number Theory. 2017; 5(5):153-158. doi: 10.12691/tjant-5-5-2.

Correspondence to: Walid  Wannes, Faculté des sciences de Sfax, BP 1171, Sfax 3000, Tunisie. Email: wannes.walid.fss@gmail.com

Abstract

Let be a positive integer and be the sum of the digits in basis q of the positive integer n. We prove that the quotient has a normal order one, where and are respectively, the number of distinct prime factors and the number of prime factors p of a positive integer n counted with multiplicity such that mod Moreover, we discuss sums of the form where f is a multiplicative function.

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