The number of prime factors of integers with dense divisors

被引：4

作者：

Weingartner, Andreas ^{[1
]}

机构：

[1] Southern Utah Univ, Dept Math, 351 West Univ Blvd, Cedar City, UT 84720 USA

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 239卷

关键词：

Normal order; Number of prime factors; Dense divisors; PRACTICAL NUMBERS; SIEVE PROBLEM;

D O I：

10.1016/j.jnt.2021.11.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for integers n, whose ratios of consecutive divisors are bounded above by an arbitrary constant, the normal order of the number of prime factors is C log log n, where C = (1 - e(-gamma))(-1)= 2.280... and gamma is Euler's constant. We explore several applications and resolve a conjecture of Margenstern about practical numbers. (c) 2021 Elsevier Inc. All rights reserved.

引用

页码：57 / 77

页数：21

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