The constant factor in the asymptotic for practical numbers
Abstract
An integer $n\ge 1$ is said to be practical if every natural number $ m \le n$ can be expressed as a sum of distinct positive divisors of $n$. The number of practical numbers up to $x$ is asymptotic to $c x/\log x$, where $c$ is a constant. In this note we show that $c=1.33607...$.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.07819
- arXiv:
- arXiv:1906.07819
- Bibcode:
- 2019arXiv190607819W
- Keywords:
-
- Mathematics - Number Theory;
- 11N25;
- 11N37
- E-Print:
- 10 pages