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 A324325 Number of non-crossing multiset partitions of a multiset whose multiplicities are the prime indices of n. 1
 1, 1, 2, 2, 3, 4, 5, 5, 9, 7, 7, 11, 11, 12, 16, 14, 15, 26, 22, 21, 29, 19, 30, 33, 31, 30, 66, 38, 42, 52, 56, 42, 47, 45, 57, 82, 77, 67, 77, 67, 101, 98, 135, 64, 137, 97, 176, 104, 109, 109, 118, 105, 231, 213, 97, 127, 181, 139, 297, 173, 385, 195, 269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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}. A multiset partition is crossing if it contains two blocks of the form {{...x...y...},{...z...t...}} where x < z < y < t or z < x < t < y. LINKS FORMULA a(n) + A324326(n) = A318284(n). EXAMPLE The a(16) = 14 non-crossing multiset partitions of the multiset {1,2,3,4}:   {{1,2,3,4}}   {{1},{2,3,4}}   {{2},{1,3,4}}   {{3},{1,2,4}}   {{4},{1,2,3}}   {{1,2},{3,4}}   {{1,4},{2,3}}   {{1},{2},{3,4}}   {{1},{3},{2,4}}   {{1},{4},{2,3}}   {{2},{3},{1,4}}   {{2},{4},{1,3}}   {{3},{1,2},{4}}   {{1},{2},{3},{4}} Missing from this list is {{1,3},{2,4}}. MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; nonXQ[stn_]:=!MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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Last modified June 12 14:45 EDT 2021. Contains 344957 sequences. (Running on oeis4.)