A Cameron and Erd\"os conjecture on counting primitive sets

Let $f(n)$ count the number of subsets of $\{1,\mathrm{.}\mathrm{.}\mathrm{.},n\}$ 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 ${\lim }_{n\to \mathrm{\infty }}f(n{)}^{1\mathrm{/}n}$ exists. This confirms a conjecture of Cameron and Erd"os, proposed in a paper where they studied a number of similar problems, including the well known “Cameron-Erd"os os Conjecture” on counting sum-free subsets.