A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions
Emil Daniel Schwab, Gabriela Schwab
Received July 18, 2022. Published online April 11, 2023.
Abstract: A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.
Affiliations: Emil Daniel Schwab (corresponding author), The University of Texas at El Paso, 500 West University Avenue, El Paso, Texas 79968, USA, e-mail: email@example.com; Gabriela Schwab, El Paso Community College, 9050 Viscount Blvd., El Paso, Texas 79902, USA, e-mail: firstname.lastname@example.org