

A322260


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


2



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

1,2


COMMENTS

This multiset (row n of A305936) is generally not the same as the multiset of prime indices of n. 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 nonlattices (n = 10, 11, ..., 15).


CROSSREFS

Cf. A001055, A007716, A057716, A265947, A281113, A305936, A317144, A317534, A318284.
Sequence in context: A133059 A132722 A048407 * A133504 A108971 A179977
Adjacent sequences: A322257 A322258 A322259 * A322261 A322262 A322263


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Dec 05 2018


STATUS

approved



