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arXiv · 2211.05819

An Erd\H{o}s-Kac theorem for integers with dense divisors

Gérald Tenenbaum·Andreas Weingartner
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Abstract

We show that for large integers $n$, whose ratios of consecutive divisors are bounded above by an arbitrary constant, the number of prime factors follows an approximate normal distribution, with mean $C \log_2 n$ and variance $V \log_2 n$, where $C=1/(1-e^{-\gamma})\approx 2.280$ and $V\approx 0.414$. This result is then generalized in two different directions.

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Gérald Tenenbaum, Andreas Weingartner. 2022-11-10. An Erd\H{o}s-Kac theorem for integers with dense divisors. https://arxiv.org/abs/2211.05819

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