Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-29T10:48:41.678Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Formulas for Some Arithmetic Functions

Published online by Cambridge University Press:  20 November 2018

P. Erdős
P. Erdős*
Affiliation:
University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f(x) be an increasing function. Recently there have been several papers which proved that under fairly general conditions on f(x) the density of integers n for which (n, f(n)) = 1 is 6/π2 and that (d(n) denotes the number of divisors of n)

In particular both of these results hold if f(x) = xα, 0 < α < 1 and the first holds if f(x) = [α x], α irrational.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 1 , Issue 3 , 01 September 1958 , pp. 149 - 153
Copyright
Copyright © Canadian Mathematical Society 1958

References

1) See Watson, G.L., Canadian Journal of Math. 5 (1953), 451-455 CrossRefGoogle Scholar, Estermann, T., ibid 5 (1953), 456-459 Google Scholar and Lambek, J. and Moser, Lr., ibid 7 (1955), 155-158.Google Scholar See also a forthcoming paper by P. Erdős and G.G. Lorentz in Acta Arithmetica.