Abstract
A natural number n is called y-smooth (y-powersmooth, respectively) for a positive number y if every prime (prime power) dividing n is bounded from above by y. Let ψ(x, y) and ψ*(x, y) denote the quantity of y-smooth and y-powersmooth integers restricted by x, respectively. In this paper we investigate function ψ*(x, y) in general. We derive formulas for finding exact calculation of ψ*(x, y) for large x and relatively small y and give theoretical estimates for this function and for a function of the greatest powersmooth integer. This results can be used in the cryptography and number theory to estimate the convergence of factorization algorithms.
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Original Russian Text © F.F. Sharifullina, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 11, pp. 60–67.
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Sharifullina, F.F. On powersmooth numbers. Russ Math. 61, 53–59 (2017). https://doi.org/10.3103/S1066369X1711007X
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DOI: https://doi.org/10.3103/S1066369X1711007X