Nov\'ak-Carmichael numbers and shifted primes without large prime factors
| Autor: | Kalmynin, Alexander |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove some new lower bounds for the counting function $\mathcal N_{\mathcal C}(x)$ of the set of Nov\'ak-Carmichael numbers. Our estimates depend on the bounds for the number of shifted primes without large prime factors. In particular, we prove that $\mathcal N_{\mathcal C}(x) \gg x^{0.7039-o(1)}$ unconditionally and that $\mathcal N_{\mathcal C}(x) \gg xe^{-(7+o(1))(\log x)\frac{\log\log\log x}{\log\log x}}$, under some reasonable hypothesis. Comment: 7 pages |
| Databáze: | arXiv |
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