

A322528


Number of integer partitions of n whose parts all have the same number of prime factors (counted with multiplicity) and whose product of parts is a power of a squarefree number (A072774).


4



1, 1, 2, 2, 3, 3, 4, 3, 5, 4, 7, 2, 7, 4, 7, 7, 9, 3, 10, 5, 12, 9, 8, 6, 14, 10, 12, 10, 14, 11, 20, 13, 18, 13, 16, 16, 25, 16, 19, 20, 26, 18, 30, 19, 27, 26, 27, 22, 38, 30, 37, 28, 38, 32, 43, 37, 46, 40, 47, 40, 66, 49, 58, 56, 64, 56, 73, 58, 76, 70, 85
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OFFSET

0,3


LINKS



EXAMPLE

The a(1) = 1 through a(8) = 5 integer partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (32) (33) (52) (44)
(1111) (11111) (222) (1111111) (53)
(111111) (2222)
(11111111)


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And[SameQ@@PrimeOmega/@#, SameQ@@Last/@FactorInteger[Times@@#]]&]], {n, 30}]


CROSSREFS

Cf. A002865, A003963, A005117, A064573 , A072774, A295193, A302505, A306017, A319169, A320322, A322526, A322527, A322529, A322530, A322531.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



