The Error Term for the Squarefree Integers

Abstract

Let Q(x) denote the number of squarefree integers ≤ x. Recently K. Rogers [ l ] has shown that Q(x) ≥ 53x / 88 for all x, with equality only at x = 176. Define R(x) to be Q(x) - 6/п2 X. (We observe that and ) Our objective will be to examine R(x). In particular, we show that for all x and observe that for x ≥ 8.