Vol. 59, No. 2, 1975

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Distribution of squarefree integers in non-linear sequences

Ivan Ernest Stux

Vol. 59 (1975), No. 2, 577–584
Abstract

I. This paper investigates the occurrences of the square-free integers in sequences sn = [f(n)],n = 1,2,8, where f(x) belongs to classes of functions described by ‘smoothness’ conditions. The result obtained is an extention of the well known fact that Q(x) = 6∕π2x + O(X12), where Q(x) = number of squarefree integers x; it states that Qs(x) 6∕π2g(x) where Q𝜖(x) = number of squarefree integers x in the sequence sn, and g(x) is the inverse function of f(x).

Mathematical Subject Classification
Primary: 10H20
Secondary: 10F40
Milestones
Received: 30 June 1975
Published: 1 August 1975
Authors
Ivan Ernest Stux