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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Wikipedia, Lattice (order) 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. CROSSREFS Cf. A001055, A007716, A025487, A045778, A065036, A162247, A265947, A281113, A317142, A317144, A317145, A317146. Sequence in context: A334589 A334936 A102374 * A240068 A269424 A319928 Adjacent sequences:  A317531 A317532 A317533 * A317535 A317536 A317537 KEYWORD nonn AUTHOR Gus Wiseman, Jul 30 2018 STATUS approved

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Last modified January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)