What percentage of numbers can be written as $n=p*m$ with p prime and $p>m$

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What is the chance* that a random positive integer $n$ is the product of a prime $p$ and an integer $m>0$, with $p>m$

Or in other words: when $n$ has a prime factor greater than it's square root

  • more formally, the amount of numbers up to N satisfying the condition, divided by N, and then letting N go to infinity.

From simulations it seems that: chance* $= 0.718 =$(?) $ 2-e$