An upper bound for the moments of a GCD related to Lucas sequences

DOI10.1216/RMJ-2019-49-3-887zbMath1418.11027arXiv1805.02225OpenAlexW2963807235MaRDI QIDQ2315283

Daniele Mastrostefano

Publication date: 2 August 2019

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.02225

zbMATH Keywords

Lucas sequencesGCD functionmoments of arithmetic functions

Mathematics Subject Classification ID

Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Other results on the distribution of values or the characterization of arithmetic functions (11N64) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (2)

Greatest common divisors of shifted primes and Fibonacci numbers ⋮ On the greatest common divisor of n and the nth Fibonacci number, II

Cites Work

• On a problem of Oppenheim concerning Factorisatio Numerorum
• The moments of the logarithm of a G.C.D. related to Lucas sequences
• The density of numbers \(n\) having a prescribed G.C.D. with the \(n\)th Fibonacci number
• On the greatest common divisor of \(n\) and the \(n\)th Fibonacci number
• On numbers \(n\) relatively prime to the \(n\)th term of a linear recurrence
• The Distribution of Self-Fibonacci Divisors
• The Period, Rank, and Order of the (a, b)-Fibonacci Sequence Mod m
• On numbers n dividing the nth term of a linear recurrence
• On numbers n dividing the nth term of a Lucas sequence
• The terms in Lucas sequences divisible by their indices
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