cp's OEIS Frontend

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

%I A299201 #14 Apr 04 2025 22:28:55
%S A299201 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 A299201 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 A299201 1,4,2,6,1,19,1,2,4,4,2,5,1,13,5,2,1,13,2
%N A299201 Number of twice-partitions whose composite is the integer partition with Heinz number n.
%C A299201 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A299201 Robert Price, <a href="/A299201/b299201.txt">Table of n, a(n) for n = 1..200</a>
%e A299201 The a(36) = 11 twice-partitions:
%e A299201   (2211),
%e A299201   (22)(11), (211)(2), (221)(1), (21)(21),
%e A299201   (2)(2)(11), (2)(11)(2), (11)(2)(2), (22)(1)(1), (21)(2)(1),
%e A299201   (2)(2)(1)(1).
%t A299201 nn=100;
%t A299201 ptns=Table[If[n===1,{},Join@@Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]],{n,nn}];
%t A299201 tris=Join@@Map[Tuples[IntegerPartitions/@#]&,ptns];
%t A299201 Table[Length[Select[tris,Sort[Join@@#,Greater]===y&]],{y,ptns}]
%Y A299201 Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299200, A299202, A299203.
%K A299201 nonn
%O A299201 1,4
%A A299201 _Gus Wiseman_, Feb 05 2018