On the Growth of Some Functions Related to z ( n )

Pavel Trojovský
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Pavel Trojovský: Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 6, 1-8

Abstract: The order of appearance z : Z > 0 → Z > 0 is an arithmetic function related to the Fibonacci sequence ( F n ) n . This function is defined as the smallest positive integer solution of the congruence F k ≡ 0 ( mod n ) . In this paper, we shall provide lower and upper bounds for the functions ∑ n ≤ x z ( n ) / n , ∑ p ≤ x z ( p ) and ∑ p r ≤ x z ( p r ) .

Keywords: asymptotic; arithmetic functions; inequalities; Fibonacci sequence; order of appearance; Landau symbols (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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