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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 (list; graph; refs; listen; history; text; internal format)
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 non-lattices (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

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Last modified January 28 03:49 EST 2020. Contains 331317 sequences. (Running on oeis4.)