Hameed, N. A., & Al-Maamori, F. (2023). Using Liouville’s function for creating weird numbers from reals. Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 123–129.
- ISSN: 2587-2648
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Nagham A. Hameeda, Faez Al-Maamorib
a Department of Mathematics, University of Babylon, Babylon, Iraq.
b Department of Security, IT College, University of Babylon, Babylon, Iraq.
In 1937, Beurling demonstrated that any positive, infinitely increasing real sequence with its first element greater than one could define a new class of integers, now known as Beurling primes. The corresponding Beurling integers (or generalized integers) can be constructed using the fundamental theorem of arithmetic. Later, Diamond extended these concepts to generalize classical arithmetic functions for primes and integers.
In this work, we propose a method to generate a new class of weird numbers (or possibly primitive weird numbers) from sufficiently large real numbers using Liouville’s function and Möbius inversion formulas related to the Pci function. The study also includes an algorithmic approach for generating these weird numbers. This work has potential applications in mathematical modeling, data simulation, and security systems.
Keywords: Analytic number theory; Data simulation; Modeling; Generalized prime systems.
Hameed, N. A., & Al-Maamori, F. (2023). Using Liouville’s function for creating weird numbers from reals. Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 123–129.