A322260 Numbers k such that the poset of multiset partitions of a multiset whose multiplicities are the prime indices of k is a lattice.

1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 32

Offset

1,2

Comments

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}.

References

R. P Stanley, Enumerative Combinatorics Vol. 1, Sec. 3.3.

Links

Table of n, a(n) for n=1..11.

Wikipedia, Lattice (order)

Gus Wiseman, The first 9 lattices (n = 1, 2, ..., 9).

Gus Wiseman, The first 6 non-lattices (n = 10, 11, ..., 15).

Crossrefs

Cf. A001055, A007716, A057716, A265947, A281113, A305936, A317144, A317534, A318284.

Sequence in context: A132722 A334828 A048407 * A133504 A335492 A108971

Adjacent sequences: A322257 A322258 A322259 * A322261 A322262 A322263

Keyword

nonn,more

Author

Gus Wiseman, Dec 05 2018

Status

approved