Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2017, 5(5), 153-158
DOI: 10.12691/tjant-5-5-2
Open AccessArticle

Sums over Numbers with Restricted Prime Factors

Khadija Mbarki1 and Walid Wannes2,

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

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

Pub. Date: July 12, 2017

Cite this paper:
Khadija Mbarki and 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

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.

Keywords:
sum-of-digits function uniform distribution modulo1 multiplicative function

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