Sums over Numbers with Restricted Prime Factors

Khadija Mbarki¹ and Walid Wannes^2,

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

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

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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