Ψ(x, y) denotes the number of positive integers ≤ x and free of prime factors > y. Hildebrand and Tenenbaum provided a good approximation of Ψ(x, y). However, their method requires the solution α = α(x, y) to the equation ∑ p≤y log p/(p α−1) = log x, and therefore it needs a large amount of time for the numerical solution of the above equation for large y… (More)

@article{Suzuki2004AnEF,
title={An estimate for the number of integers without large prime factors},
author={Koji Suzuki},
journal={Math. Comput.},
year={2004},
volume={73},
pages={1013-1022}
}