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.
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页码：57 / 77
页数：21
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