A Cameron and Erdös conjecture on counting primitive sets

Abstract

Let $f(n)$ count the number of subsets of $\{1,...,n\}$ without an element dividing another. In this paper I show that $f(n)$ grows like the $n$-th power of some real number, in the sense that ${\lim }_{n\to \infty }f(n{)}^{1/n}$ exists. This confirms a conjecture of Cameron and Erdös, proposed in a paper where they studied a number of similar problems, including the well known "Cameron-Erdös os Conjecture" on counting sum-free subsets.

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• Errata and Addenda to Mathematical Constants