How many of the composite numbers are multiples of squares:
Let $C(n) =$ all composite numbers $\le n$
Let $\mu_0(n) =$ the number of integers $\le n$ with a value of $\mu =0$
$${\mu_0(n) \over C(n)} \thicksim (??) $$
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3Integers with $\mu \ne 0$ are said to be squarefree. It is a "well-known" result that $$\lim_{n \to \infty} \frac{n-\mu_0(n)}{n} = \frac{6}{\pi^2}$$ And of course $C(n)/n \to 1$, so your limit is $1 - 6/\pi^2$. – Robert Israel Dec 28 '23 at 03:19
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@RobertIsrael Thank you. It's the inverse of the basel problem? – Older Amateur Dec 28 '23 at 03:24
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Yes, see the Distribution section at the Wikipedia link I gave. – Robert Israel Dec 28 '23 at 03:28