تقرير
On practical sets and $A$-practical numbers
| العنوان: | On practical sets and $A$-practical numbers |
|---|---|
| المؤلفون: | Kukla, Andrzej, Miska, Piotr |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | Let $A$ be a set of positive integers. We define a positive integer $n$ as an $A$-practical number if every positive integer from the set $\left\{1,\ldots ,\sum_{d\in A, d\mid n}d\right\}$ can be written as a sum of distinct divisors of $n$ that belong to $A$. Denote the set of $A$-practical numbers as $\text{Pr}(A)$. The aim of the paper is to explore the properties of the sets $\text{Pr}(A)$ (the form of the elements, cardinality) as $A$ varies over the power set of $\mathbb{N}$. We are also interested in the set-theoretic and dynamic properties of the mapping $\mathcal{PR}:\mathcal{P}(\mathbb{N})\ni A\mapsto\text{Pr}(A)\in\mathcal{P}(\mathbb{N})$. Comment: This is a preliminary version of the paper |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.18225 |
| رقم الأكسشن: | edsarx.2405.18225 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |