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Asymptotic Formulas for Some Arithmetic Functions

Published online by Cambridge University Press:  20 November 2018

P. Erdős
P. Erdős*
Affiliation:
University of British Columbia
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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.