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arXiv · 1706.07343

Nov\'ak-Carmichael numbers and shifted primes without large prime factors

Alexander Kalmynin
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Abstract

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.

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Alexander Kalmynin. 2017-06-22. Nov\'ak-Carmichael numbers and shifted primes without large prime factors. https://arxiv.org/abs/1706.07343

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