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arXiv · 1808.04923

Counting primitive subsets and other statistics of the divisor graph of $\{1,2, \ldots n\}$

Nathan McNew
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Abstract

Let $Q(n)$ denote the count of the primitive subsets of the integers $\{1,2\ldots n\}$. We give a new proof that $Q(n) = \alpha^{(1+o(1))n}$ which allows us to give a good error term and to improve upon the lower bound for the value of this constant $\alpha$. We also show that the method developed can be applied to many similar problems that can be stated in terms of the divisor graph, including other questions about primitive sets, geometric-progression-free sets, and the divisor graph path-cover problem.

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Nathan McNew. 2018-08-14. Counting primitive subsets and other statistics of the divisor graph of $\{1,2, \ldots n\}$. https://arxiv.org/abs/1808.04923

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