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arXiv · 2102.06127

The natural density of some sets of square-free numbers

Ron Brown
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Abstract

Let $P$ and $T$ be disjoint sets of prime numbers with $T$ finite. A simple formula is given for the natural density of the set of square-free numbers which are divisible by all of the primes in $T$ and by none of the primes in $P$. If $P$ is the set of primes congruent to $r$ modulo $m$ (where $m$ and $r$ are relatively prime numbers), then this natural density is shown to be $0$.

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Ron Brown. 2021-02-09. The natural density of some sets of square-free numbers. https://arxiv.org/abs/2102.06127

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