The largest prime factor of Landau's function

DOI10.1007/s11139-011-9293-2zbMath1276.11157OpenAlexW1973298275MaRDI QIDQ662898

Jean Louis Nicolas, Marc Deléglise

Publication date: 13 February 2012

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-011-9293-2

zbMATH Keywords

symmetric groupdistribution of primesmaximal orderLandau's function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Asymptotic results on counting functions for algebraic and topological structures (11N45) Arithmetic functions; related numbers; inversion formulas (11A25) Distribution of primes (11N05) Symmetric groups (20B30)

Related Items (3)

Maximal product of primes whose sum is bounded ⋮ Highly composite numbers and the Riemann hypothesis ⋮ AN ARITHMETIC EQUIVALENCE OF THE RIEMANN HYPOTHESIS

Cites Work

• Landau's function for one million billions
• Highly composite numbers. Annotated by Jean-Louis Nicolas and Guy Robin
• Short effective intervals containing primes
• Approximate formulas for some functions of prime numbers
• The Difference Between Consecutive Primes, II
• The Maximum Order of an Element of a Finite Symmetric Group
• Majoration explicite de l'ordre maximum d'un élément du groupe symétrique
• Évaluation asymptotique de l'ordre maximum d'un élément du groupe symétrique
• Effective Bounds for the Maximal Order of an Element in the Symmetric Group
• On the maximal order in $S_n$ and $S*_n$
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2
• New maximal prime gaps and first occurrences
• The Largest Prime Dividing the Maximal Order of an Element of S n
• Ordre maximal d'un élément du groupe $S_n$ des permutations et «highly composite numbers»
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