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

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) . [ABSTRACT FROM AUTHOR]