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A317534
Numbers k such that the poset of factorizations of k, ordered by refinement, is not a lattice.
3
24, 32, 40, 48, 54, 56, 60, 64, 72, 80, 84, 88, 90, 96, 104, 108, 112, 120, 126, 128, 132, 135, 136, 140, 144, 150, 152, 156, 160, 162, 168, 176, 180, 184, 189, 192, 198, 200, 204, 208, 216, 220, 224, 228, 232, 234, 240, 243, 248, 250, 252, 256, 260, 264, 270
OFFSET
1,1
COMMENTS
Includes 2^k for all k > 4.
Conjecture: Let S be the set of all numbers whose prime signature is either {1,3}, {5}, or {1,1,2}. Then the sequence consists of all multiples of elements of S. - David A. Corneth, Jul 31 2018.
REFERENCES
R. P Stanley, Enumerative Combinatorics Vol. 1, Sec. 3.3.
EXAMPLE
In the poset of factorizations of 24, the factorizations (2*2*6) and (2*3*4) have two least-upper bounds, namely (2*12) and (4*6), so this poset is not a lattice.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 30 2018
STATUS
approved