On an inequality in the elementary theory of numbers

Author:

Heilbronn H. A.

Abstract

Let a1, a2, …, an be a set of n positive integers. Then it is easily seen that the set of positive integers not divisible by any aν has a density, i.e. that if Nn(z) is the number of such integers not exceeding z, then z−1Nn(z) tends to a limit when z → ∞; and thatwhereand where [u1, …, uμ] denotes the least positive common multiple of the positive integers u1, …, uμ.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 20 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A SHARP UPPER BOUND FOR THE SUM OF RECIPROCALS OF LEAST COMMON MULTIPLES II;Bulletin of the Australian Mathematical Society;2022-06-09

2. Corrigendum to “Artin's primitive root conjecture for function fields revisited” [Finite Fields Appl. 67 (2020) 101713];Finite Fields and Their Applications;2022-02

3. On the sum of reciprocals of least common multiples, II;Applied Mathematics and Computation;2021-06

4. A sharp upper bound for the sum of reciprocals of least common multiples;Acta Mathematica Hungarica;2019-09-04

5. A note on primes in certain residue classes;International Journal of Number Theory;2018-08-22

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