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arXiv · 2504.02699

An extension of smooth numbers: multiple dense divisibility

Garo Sarajian·Andreas Weingartner
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Abstract

The $i$-tuply $y$-densely divisible numbers were introduced by a Polymath project, as a weaker condition on the moduli than $y$-smoothness, in distribution estimates for primes in arithmetic progressions. We obtain the order of magnitude of the count of these integers up to $x$, uniformly in $x$ and $y$, for every fixed natural number $i$.

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Garo Sarajian, Andreas Weingartner. 2025-04-03. An extension of smooth numbers: multiple dense divisibility. https://arxiv.org/abs/2504.02699

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