%I #7 Feb 23 2018 11:10:29
%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