An estimate for the number of integers without large prime factors

Abstract

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)
DOI: 10.1090/S0025-5718-03-01571-0

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Cite this paper

@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} }