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A299201 Number of twice-partitions whose composite is the integer partition with Heinz number n. 19

%I

%S 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,

%T 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,

%U 1,4,2,6,1,19,1,2,4,4,2,5,1,13,5,2,1,13,2

%N Number of twice-partitions whose composite is the integer partition with Heinz number n.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%e The a(36) = 11 twice-partitions:

%e (2211),

%e (22)(11), (211)(2), (221)(1), (21)(21),

%e (2)(2)(11), (2)(11)(2), (11)(2)(2), (22)(1)(1), (21)(2)(1),

%e (2)(2)(1)(1).

%t nn=100;

%t ptns=Table[If[n===1,{},Join@@Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]],{n,nn}];

%t tris=Join@@Map[Tuples[IntegerPartitions/@#]&,ptns];

%t Table[Length[Select[tris,Sort[Join@@#,Greater]===y&]],{y,ptns}]

%Y Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299200, A299202, A299203.

%K nonn

%O 1,4

%A _Gus Wiseman_, Feb 05 2018

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Last modified February 20 12:04 EST 2020. Contains 332076 sequences. (Running on oeis4.)