The constant factor in the asymptotic for practical numbers-Reference-Cited by-同舟云学术

The constant factor in the asymptotic for practical numbers

Published:2019-09-30 Issue:03 Volume:16 Page:629-638
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Weingartner Andreas¹

Affiliation:

1. Department of Mathematics, Southern Utah University, 351 West University Boulevard, Cedar City, Utah 84720, USA

Abstract

An integer [Formula: see text] is said to be practical if every natural number [Formula: see text] can be expressed as a sum of distinct positive divisors of [Formula: see text]. The number of practical numbers up to [Formula: see text] is asymptotic to [Formula: see text], where [Formula: see text] is a constant. In this paper, we show that [Formula: see text]

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500311

Reference11 articles.

1. An analytic method for bounding 𝜓(𝑥)

2. Explicit estimates of some functions over primes

3. Les nombres pratiques: théorie, observations et conjectures

4. Approximate formulas for some functions of prime numbers

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