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).

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

Offset

0,3

Links

Table of n, a(n) for n=0..70.

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.

Sequence in context: A205561 A323636 A283367 * A258756 A127431 A289777

Adjacent sequences: A322525 A322526 A322527 * A322529 A322530 A322531

Keyword

nonn

Author

Gus Wiseman, Dec 14 2018

Extensions

More terms from Alois P. Heinz, Dec 14 2018

Status

approved