Two questions:
- Is there a name for integers $n$ having no prime factors exceeding $\sqrt n$?
- What results say something about the frequency with which these occur? For example, if $A$ is the set of such numbers, then might $\displaystyle\lim_{n\to\infty}\frac{|A\cap\{1,\ldots,n\}|} n$ exist? Or liminf and limsup? Or maybe $\displaystyle\lim_{n\to\infty}\frac{|A\cap\{1,\ldots,n\}|} n g(n)$ exists for some specified function $g$? Etc. (A few not-really-random samples of numbers less than $10^5$ suggest maybe a bit more than a quarter of those are in $A$.)