The question regarding is: which position out of k-dim numbers does it have? We see that 3 is the first prime, i.e. num of dimension 1, 9 is just after 6, 27 is after {12, 18, 20}, 81 after {24, 36, 40, 54, 56, 60} etc. So, before we have 1, 3, 6, 12, 21,.. From there, one might notice that for k-th column this number is formed via summation of the numbers of blockers in all previous columns. And to answer the question in the introduction, we just need to add 1 to those numbers, i.e. (1),2 ,4 , 7, 13, 22,.., that is e.g. 3^6 is the 22th number with 6 non-distinct divisors (dim=6). I skipped proceeding with this for today as I played with yet another thing, shown below.

Below, the amount of primes without even digits. Bumped into this idea to take a look at it, here it is.

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Imagine a story that one can't believe. Hi. Life changes here. Small things only.