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A322526
Number of integer partitions of n whose product of parts is a squarefree number.
8
1, 1, 2, 3, 3, 5, 6, 8, 9, 10, 13, 15, 17, 21, 24, 27, 30, 36, 41, 46, 51, 57, 65, 73, 82, 90, 101, 109, 121, 134, 150, 164, 177, 193, 214, 232, 253, 278, 300, 324, 351, 386, 419, 452, 484, 521, 563, 610, 658, 706, 758, 809, 868, 938, 1006, 1071, 1140, 1220, 1307
OFFSET
0,3
COMMENTS
The parts of such a partition must also be squarefree and distinct except for any number of 1's.
EXAMPLE
The a(8) = 9 partitions are (53), (71), (521), (611), (5111), (32111), (311111), (2111111), (11111111). Missing from this list are (8), (62), (44), (431), (422), (4211), (41111), (332), (3311), (3221), (2222), (22211), (221111).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SquareFreeQ[Times@@#]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 14 2018
STATUS
approved