A property of the counting function of integers with no large prime factors
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For logy log log x → ∞ as x → ∞, ψ(Cx, y) ≈ Cψ(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 Ψ(Cx,y)≈C1-1/KΨ(x,y). © 1986.
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