Corpus ID: 119151174

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

@article{McNew2018CountingPS,
  title={Counting primitive subsets and other statistics of the divisor graph of \$\\{1,2, \ldots n\\}\$},
  author={Nathan McNew},
  journal={arXiv: Number Theory},
  year={2018}
}
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… Expand
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