# On square-free numbers generated from given sets of primes

@article{Romn2022OnSN, title={On square-free numbers generated from given sets of primes}, author={G{\'a}bor Rom{\'a}n}, journal={Communications in Mathematics}, year={2022} }

Let $x$ be a positive real number, and $\mathcal{P} \subset [2,\lambda(x)]$
be a set of primes, where $\lambda(x) \in o(x^{1/2})$ is a monotone increasing
function. We examine $Q_{\mathcal{P}}(x)$ for different sets $\mathcal{P}$,
where $Q_{\mathcal{P}}(x)$ is the element count of the set containing those
positive square-free integers, which are smaller than-, or equal to $x$, and
which are only divisible by the elements of $\mathcal{P}$.

## 18 References

### Multiplicative Number Theory

- 1967

Mathematics

From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- The…

### Introduction to analytic number theory

- 1976

Mathematics

This is the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. It provides an introduction…

### Unsolved problems in number theory

- 2001

Mathematics

Period. Math. Hung.

The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences, arithmetic functions and the greatest prime factor func- tion and mixed problems.

### Introduction To Cyclotomic Fields

- 2016

Education

The introduction to cyclotomic fields is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.

### Über die kleinste quadratfreie Zahl einer arithmetischen Reihe

- 1958

Mathematics

Es sei (a, d) = 1, 1 e a < d. Dann gibt es eine absolute Konstante c, so daß die kleinste quadratfreie Zahl in der arithmetischen Progression a + k d, k = 0, 1,. .. kleiner als c d'/' /log d…

### Accepted for publication

- 1999

Computer Science

This research aims to provide wireless and distributed systems with the capability of self-monitoring, self-reconfiguration, and self-optimization at the presence of varying wireless link-quality.

### Introduction To Analytic And Probabilistic Number Theory

- 2016

Education

This introduction to analytic and probabilistic number theory is free to download and may help people find their favorite readings that end up in malicious downloads.