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

1,4

Comments

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

Links

Table of n, a(n) for n=1..85.

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: A353378 A112970 A112971 * A342085 A050379 A344589

Adjacent sequences: A299198 A299199 A299200 * A299202 A299203 A299204

Keyword

nonn

Author

Gus Wiseman, Feb 05 2018

Status

approved