Squarefree integers in nonlinear sequences

Friedrich Roesler

Vol. 123 (1986), No. 1, 223–225

DOI: 10.2140/pjm.1986.123.223

Abstract

The number of squarefree integers in sequences [f(n + x)], n = 1,2,3,…,N is (6∕π² + o(1))N for almost all x ≥ 0, when f is a polynomial function of degree k ≥ 2 or an exponential function.

Mathematical Subject Classification 2000

Primary: 11N25

Secondary: 11N37

Milestones

Received: 9 March 1979

Published: 1 May 1986