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A322529 Number of integer partitions of n whose parts all have the same number of prime factors (counted with or without multiplicity) and whose product of parts is a squarefree number. 3
1, 1, 2, 2, 1, 3, 2, 3, 2, 2, 4, 2, 3, 3, 4, 4, 4, 3, 5, 4, 5, 6, 6, 6, 6, 6, 8, 6, 7, 9, 8, 11, 8, 11, 11, 11, 12, 13, 13, 15, 13, 17, 17, 18, 18, 17, 20, 22, 21, 24, 24, 24, 26, 29, 28, 33, 30, 35, 34, 38, 38, 45, 42, 43, 45, 48, 52, 54, 55, 59 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Such a partition must be strict (unless it is all 1's) and its parts must also be squarefree.

LINKS

Table of n, a(n) for n=0..69.

EXAMPLE

The a(30) = 8 integer partitions:

  (30),

  (17,13),(19,11),(23,7),

  (17,11,2),(23,5,2),

  (13,7,5,3,2),

  (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1).

MATHEMATICA

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

CROSSREFS

Cf. A002865, A003963, A005117, A038041, A064573, A073576, A302505, A319056, A320322, A321717, A321718, A322526, A322527, A322528, A322530, A322531.

Sequence in context: A128180 A209279 A074754 * A329949 A333867 A030717

Adjacent sequences:  A322526 A322527 A322528 * A322530 A322531 A322532

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 14 2018

EXTENSIONS

a(51)-a(69) from Jinyuan Wang, Jun 27 2020

STATUS

approved

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Last modified October 27 00:02 EDT 2021. Contains 348270 sequences. (Running on oeis4.)