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arXiv · 2101.11585

The number of prime factors of integers with dense divisors

Andreas Weingartner
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Abstract

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.

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Andreas Weingartner. 2021-01-27. The number of prime factors of integers with dense divisors. https://arxiv.org/abs/2101.11585

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