

A299200


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


10



1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 11, 5, 6, 1, 15, 4, 22, 3, 10, 7, 30, 2, 9, 11, 8, 5, 42, 6, 56, 1, 14, 15, 15, 4, 77, 22, 22, 3, 101, 10, 135, 7, 12, 30, 176, 2, 25, 9, 30, 11, 231, 8, 21, 5, 44, 42, 297, 6, 385, 56, 20, 1, 33, 14, 490, 15, 60, 15, 627, 4
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OFFSET

1,3


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..72.


FORMULA

Multiplicative with a(prime(n)) = A000041(n).


EXAMPLE

The a(15) = 6 twicepartitions: (3)(2), (3)(11), (21)(2), (21)(11), (111)(2), (111)(11).


MATHEMATICA

Table[Times@@Cases[FactorInteger[n], {p_, k_}:>PartitionsP[PrimePi[p]]^k], {n, 100}]


PROG

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = numbpart(primepi(f[k, 1])); ); factorback(f); } \\ Michel Marcus, Feb 26 2018


CROSSREFS

Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299201, A299202, A299203.
Sequence in context: A064989 A290099 A250479 * A321272 A321270 A030067
Adjacent sequences: A299197 A299198 A299199 * A299201 A299202 A299203


KEYWORD

nonn,mult


AUTHOR

Gus Wiseman, Feb 05 2018


STATUS

approved



