# Sums of fractional parts and sum of restricted divisors of a number

## Main Article Content

## Abstract

Let us consider a strictly increasing sequence of positive integers *a*_{n} such that *A*(*x*) is the distribution function of the sequence. That is, *A*(*x*)=∑ _{an≤ x} 1. We study the sum ∑ _{an≤ x} *a _{n}^{s}*{

*x / a*} and apply this formula in the study of the sum of

_{n}*a*-divisors of a number. The distribution functions

*A*(

*x*) considered are very general. The methods used are very elementary.

## Article Details

How to Cite

*Gulf Journal of Mathematics*,

*10*(1), 36-42. Retrieved from https://gjom.org/index.php/gjom/article/view/552

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