Practical central binomial coefficients
| Autor: | Carlo Sanna |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Practical number Mathematics - Number Theory practical number 11B65 (Primary) 11N25 (Secondary) Mathematics (miscellaneous) Integer FOS: Mathematics Central binomial coefficient Number Theory (math.NT) Central binomial coefficient practical number Binomial coefficient Mathematics |
| Zdroj: | Quaestiones Mathematicae; Vol. 44 No. 9 (2021); 1141-1144 |
| ISSN: | 1727-933X 1607-3606 |
| DOI: | 10.2989/16073606.2020.1775156 |
| Popis: | A practical number is a positive integer $n$ such that all positive integers less than $n$ can be written as a sum of distinct divisors of $n$. Leonetti and Sanna proved that, as $x \to +\infty$, the central binomial coefficient $\binom{2n}{n}$ is a practical number for all positive integers $n \leq x$ but at most $O(x^{0.88097})$ exceptions. We improve this result by reducing the number of exceptions to $\exp\!\big(C (\log x)^{4/5} \log \log x\big)$, where $C > 0$ is a constant. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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