

A299201


Number of twicepartitions whose composite is the integer partition with Heinz number n.


19



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
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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 twicepartitions:
(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: A129138 A112970 A112971 * A050379 A153024 A066921
Adjacent sequences: A299198 A299199 A299200 * A299202 A299203 A299204


KEYWORD

nonn


AUTHOR

Gus Wiseman, Feb 05 2018


STATUS

approved



