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 A324326 Number of crossing multiset partitions of a multiset whose multiplicities are the prime indices of n. 4
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 10, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 36, 0, 14, 0, 0, 0, 25, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,24 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...}} with x < z < y < t or z < x < t < y. LINKS Table of n, a(n) for n=1..80. FORMULA a(n) + A324325(n) = A318284(n). EXAMPLE The a(36) = 10 crossing multiset partitions of {1,1,2,2,3,4}: {{1,3},{1,2,2,4}} {{2,4},{1,1,2,3}} {{1,1,3},{2,2,4}} {{1,2,3},{1,2,4}} {{1},{1,3},{2,2,4}} {{1},{2,4},{1,2,3}} {{2},{1,3},{1,2,4}} {{2},{1,1,3},{2,4}} {{1,2},{1,3},{2,4}} {{1},{2},{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]]}]]; croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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Last modified August 8 14:00 EDT 2024. Contains 375021 sequences. (Running on oeis4.)