Abstract

For k, being a fixed integer ≥2, a positive integer n is called k-free number if n is not divisible by the kth power of any integer >1. In this paper, we studied the distribution of r-tuples of k-free numbers and derived an asymptotic formula.

Highlights

  • A positive integer n is called square-free number if it is not divisible by a perfect square except 1

  • Let q2 be the characteristic function of the sequence of square-free numbers

  • Mirsky [2] studied the frequency of pairs of square-free numbers with a given difference and proved the asymptotic formula:

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Summary

Introduction

A positive integer n is called square-free number if it is not divisible by a perfect square except 1. Let q2 be the characteristic function of the sequence of square-free numbers. Q2 (n) = {10,, if n is a square-free number, otherwise. Mirsky [2] studied the frequency of pairs of square-free numbers with a given difference and proved the asymptotic formula:

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