A property of the counting function of integers with no large prime factors
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For logy log log x as x , (Cx, y) C(x, y) uniformly for C in compact subsets of (0, 1]. The condition logy log log x is necessary. For fixed sufficiently large K, x , and y = exp(K log log x), we have for 1 2 C 1 that (Cx,y)C1-1/K(x,y). 1986.