Counting primitive subsets and other statistics of the divisor graph of [formula omitted

Abstract

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