Using.Liouville’s function for Creating a weird numbers from Reals

Abstract

During 1937 Beurling Showed that any positive infinitely increasing real sequence such that the its first element precisely greater than one, called a Beurling’s primes. Furthermore, the series of Beurling integers (or generalized integers) can be constructed using the fundamental theorem of arithmetic. During the seventieth of the last century, Diamond showed that majority of the arithmetical functions were generalized to deal with the generalization of the primes and integers. This work aims to create some weird numbers from a large enough reals So, the reader has to be familiar with Mobius inversion formula of the Pci function. The challenging of this work is the dealing with an algorithm for generating a weird numbers (or maybe a primitive weird numbers) from a large enough real numbers x. The idea of this work can be used for an application of modeling, data simulation and security subjects.

Keywords

• analytic number theory
• data simulation
• modeling
• generalized prime systems