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

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

Offset: 1

Author

Gus Wiseman, Feb 05 2018

Keywords

• nonn

Comments

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

Examples

			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).
		

Links

• Robert Price, Table of n, a(n) for n = 1..200

Crossrefs

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

Programs

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}]