|
%I #18 Jul 17 2021 06:43:02
%S 24,32,40,48,54,56,60,64,72,80,84,88,90,96,104,108,112,120,126,128,
%T 132,135,136,140,144,150,152,156,160,162,168,176,180,184,189,192,198,
%U 200,204,208,216,220,224,228,232,234,240,243,248,250,252,256,260,264,270
%N Numbers k such that the poset of factorizations of k, ordered by refinement, is not a lattice.
%C Includes 2^k for all k > 4.
%C 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.
%D R. P Stanley, Enumerative Combinatorics Vol. 1, Sec. 3.3.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_(order)">Lattice (order)</a>
%e 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.
%Y Cf. A001055, A007716, A025487, A045778, A065036, A162247, A265947, A281113, A317142, A317144, A317145, A317146.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 30 2018
|
