On the composition of the Euler function and the sum of divisors function

• Autorzy: Jean-Marie De Koninck , Florian Luca
• Języki publikacji: EN

Abstrakty

EN

Let H(n) = σ(ϕ(n))/ϕ(σ(n)), where ϕ(n) is Euler's function and σ(n) stands for the sum of the positive divisors of n. We obtain the maximal and minimal orders of H(n) as well as its average order, and we also prove two density theorems. In particular, we answer a question raised by Golomb.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11A25: Arithmetic functions; related numbers; inversion formulas
• 11N56: Rate of growth of arithmetic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 1
• Strony: 31-51

Daty

wydano

2007

Twórcy

autor

Jean-Marie De Koninck

• Département de mathématiques, Université Laval, Québec G1K 7P4, Canada

autor

Florian Luca

• Mathematical Institute, UNAM, Ap. Postal 61-3(Xangari), CP 58 089, Morelia, Michoacán, Mexico

Identyfikatory

DOI

10.4064/cm108-1-4