I am looking for a chart that would show how many composite numbers there are under "n" broken out by how many factors they have. Has anyone seen a chart like this?
Example information I am looking for:
composite numbers under 20
total: 11
with 2 factors: 6
with 3 factors: 4
with 4 factors: 1
You need to learn to program the computer. It takes only a few minutes to get a computer to emit such a table. (Actually producing the table is instantaneous.)
I tabulated it up to $N=1000$ and put it here for you. (The table is too large for a SE post.) Notice line $20$, which reads $8\,6\,4\,1$, as you requested.