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A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions
Mathematica Bohemica, Tome 149 (2024) no. 2, pp. 237-246
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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.
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.
DOI : 10.21136/MB.2023.0102-22
Classification : 11A25, 11B39
Keywords: Fibonacci sequence; multiplicative arithmetic function; Binet's formula; Busche-Ramanujan identities; Möbius inversion 
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Schwab, Emil Daniel; Schwab, Gabriela. A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions. Mathematica Bohemica, Tome 149 (2024) no. 2, pp. 237-246. doi: 10.21136/MB.2023.0102-22

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