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A322530
Number of integer partitions of n with no 1's whose product of parts is a squarefree number.
7
1, 0, 1, 1, 0, 2, 1, 2, 1, 1, 3, 2, 2, 4, 3, 3, 3, 6, 5, 5, 5, 6, 8, 8, 9, 8, 11, 8, 12, 13, 16, 14, 13, 16, 21, 18, 21, 25, 22, 24, 27, 35, 33, 33, 32, 37, 42, 47, 48, 48, 52, 51, 59, 70, 68, 65, 69, 80, 87, 90, 103, 100, 96, 103, 123, 128, 135, 136, 132, 153
OFFSET
0,6
COMMENTS
Such a partition must be strict and its parts must also be squarefree.
EXAMPLE
The a(26) = 11 integer partitions:
(26),
(15,11), (19,7), (21,5), (23,3),
(13,7,6), (13,10,3), (13,11,2), (17,7,2), (19,5,2),
(11,7,5,3).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&SquareFreeQ[Times@@#]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 14 2018
STATUS
approved