Distribution of squarefree integers in non-linear sequences
Ivan Stux · Pacific Journal of Mathematics · 1975
I. This paper investigates the occurrences of the squarefree integers in sequences s n = [f(n)] t n = 1, 2, 3, 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) = β/π 2 x + 0(# 1/2 ), where Q{x) -number of squarefree integers ^ x; it states that Q s (x) ~ β/π 2 g(x) where Q 8 (x) = number of squarefree integers ^ x in the sequence s n , and g(x) is the inverse function of f(x).