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 A320659 Number of factorizations of A181821(n) into squarefree semiprimes. Number of multiset partitions, of a multiset whose multiplicities are the prime indices of n, into strict pairs. 4
 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 15, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS This multiset 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}. LINKS EXAMPLE The a(48) = 6 factorizations:   4620 = (6*10*77)   4620 = (6*14*55)   4620 = (6*22*35)   4620 = (10*14*33)   4620 = (10*21*22)   4620 = (14*15*22) The a(48) = 6 multiset partitions:   {{1,2},{1,3},{4,5}}   {{1,2},{1,4},{3,5}}   {{1,2},{1,5},{3,4}}   {{1,3},{1,4},{2,5}}   {{1,3},{2,4},{1,5}}   {{1,4},{2,3},{1,5}} MATHEMATICA nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]]; qepfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[qepfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]]; Table[Length[qepfacs[Times@@Prime/@nrmptn[n]]], {n, 100}] CROSSREFS A001147(n) = a(2^(2n)). Cf. A001222, A007716, A007717, A056239, A112798, A181821, A305936, A318284, A320655, A320656, A320658. Sequence in context: A327159 A280051 A030121 * A062535 A063667 A171063 Adjacent sequences:  A320656 A320657 A320658 * A320660 A320661 A320662 KEYWORD nonn AUTHOR Gus Wiseman, Oct 18 2018 STATUS approved

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Last modified September 25 13:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)