Nonaliquots and Robbins numbers

• Autorzy: William D. Banks , Florian Luca
• Języki publikacji: EN

Abstrakty

EN

Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. We give a lower bound for the number of m ≤ x for which the equation m = σ(n) - n has no solution. We also show that the set of positive integers m not of the form (p-1)/2 - φ(p-1) for some prime number p has a positive lower asymptotic density.

Kategorie tematyczne

• 11A25: Arithmetic functions; related numbers; inversion formulas
• 11A41: Primes
• 11N64: Other results on the distribution of values or the characterization of arithmetic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 103
• Numer: 1
• Strony: 27-32

Daty

wydano

2005

Twórcy

autor

William D. Banks

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

autor

Florian Luca

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México

Identyfikatory

DOI

10.4064/cm103-1-4