OEIS (A028442) lists the Numbers n such that Mertens' function
$ M(n)=\sum_{k=1}^n\mu(k) $ is zero:
2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427,...
Do these numbers have a deeper significance other than: The set of numbers below $n$ is split into $2$ equally large sets with $\mu(m\le n)=\pm 1$ (with asymptotic density each $\frac{3}{\pi^2}$) and the set $\mu(m\le n)=0$ (with asymptotic density $1-\frac{6}{\pi^2}$)?
I mean, does the fact that $\lim_{n\to\infty}M(n)=0$ play a role (whatever that is in the infinite case) in a finite case as well? I'm especially interested in the case where $n$ is even.