On powersmooth numbers
| Autor: | F. F. Sharifullina |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Russian Mathematics. 61:53-59 |
| ISSN: | 1934-810X 1066-369X |
| DOI: | 10.3103/s1066369x1711007x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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