Integers without divisors from a fixed arithmetic progression

DOI10.1515/FORUM.2008.045zbMath1257.11002arXivmath/0604036OpenAlexW2015575150MaRDI QIDQ3546143

William D. Banks, Florian Luca, John B. Friedlander

Publication date: 18 December 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604036

zbMATH Keywords

divisorarithmetic progressionasymptotic formula

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (5)

Distribution of root numbers of Hecke characters attached to some elliptic curves ⋮ When the nontrivial, small divisors of a natural number are in arithmetic progression ⋮ Integers without divisors in a given progression ⋮ When the Large Divisors of a Natural Number Are in Arithmetic Progression ⋮ Unnamed Item

Cites Work

• Das asymptotische Verhalten von Summen über multiplikative Funktionen
• On a problem of Oppenheim concerning Factorisatio Numerorum
• On the number of positive integers \(\leq x\) and free of prime factors \(>y\)
• On some conjectures of Erdős in Astérisque. I
• Sets of multiples of finite sequences
• Mertens' theorem for arithmetic progressions
• Proof of a conjecture about the distribution of divisors of integers in residue classes
• Répartition Des Diviseurs Dans Les Progressions Arithmétiques
• Shorter Notes: On Some Products Involving Primes

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