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%I #26 Jul 17 2021 11:23:38
%S 1,2,3,4,5,6,7,8,9,16,32
%N Numbers k such that the poset of multiset partitions of a multiset whose multiplicities are the prime indices of k is a lattice.
%C This multiset (row k of A305936) is generally not the same as the multiset of prime indices of k. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
%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>
%H Gus Wiseman, <a href="/A322260/a322260.png">The first 9 lattices (n = 1, 2, ..., 9).</a>
%H Gus Wiseman, <a href="/A322260/a322260_1.png">The first 6 non-lattices (n = 10, 11, ..., 15).</a>
%Y Cf. A001055, A007716, A057716, A265947, A281113, A305936, A317144, A317534, A318284.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Dec 05 2018
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