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

Author

Gus Wiseman, Dec 05 2018

Keywords

• nonn
• more

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

• 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.