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 A299201 Number of twice-partitions whose composite is the integer partition with Heinz number n. 19
 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 5, 1, 2, 2, 5, 1, 4, 1, 4, 2, 2, 1, 8, 2, 2, 3, 4, 1, 6, 1, 7, 2, 2, 2, 11, 1, 2, 2, 8, 1, 5, 1, 4, 4, 2, 1, 16, 2, 4, 2, 4, 1, 7, 2, 7, 2, 2, 1, 13, 1, 2, 5, 11, 2, 5, 1, 4, 2, 6, 1, 19, 1, 2, 4, 4, 2, 5, 1, 13, 5, 2, 1, 13, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS EXAMPLE The a(36) = 11 twice-partitions: (2211), (22)(11), (211)(2), (221)(1), (21)(21), (2)(2)(11), (2)(11)(2), (11)(2)(2), (22)(1)(1), (21)(2)(1), (2)(2)(1)(1). MATHEMATICA nn=100; ptns=Table[If[n===1, {}, Join@@Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]], {n, nn}]; tris=Join@@Map[Tuples[IntegerPartitions/@#]&, ptns]; Table[Length[Select[tris, Sort[Join@@#, Greater]===y&]], {y, ptns}] CROSSREFS Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299200, A299202, A299203. Sequence in context: A129138 A112970 A112971 * A050379 A153024 A066921 Adjacent sequences:  A299198 A299199 A299200 * A299202 A299203 A299204 KEYWORD nonn AUTHOR Gus Wiseman, Feb 05 2018 STATUS approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)