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

Author

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  • Pavel Trojovský

    (Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic)

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 ) .

Suggested Citation

  • Pavel Trojovský, 2020. "On the Growth of Some Functions Related to z ( n )," Mathematics, MDPI, vol. 8(6), pages 1-8, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:876-:d:365669
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    References listed on IDEAS

    as
    1. Matt Visser, 2018. "Primes and the Lambert W function," Mathematics, MDPI, vol. 6(4), pages 1-6, April.
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