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A325039
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Number of integer partitions of n with the same product of parts as their conjugate.
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20
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1, 1, 0, 1, 1, 1, 1, 1, 6, 2, 2, 4, 3, 5, 7, 6, 5, 7, 9, 10, 11, 18, 16, 19, 19, 16, 20, 20, 28, 39, 28, 40, 53, 45, 52, 59, 71, 61, 73, 97, 102, 95, 112, 131, 137, 148, 140, 166, 199, 181, 238, 251, 255, 289, 339, 344, 381, 398, 422, 464, 541, 555, 628, 677, 732
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OFFSET
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0,9
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COMMENTS
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For example, the partition (6,4,1) with product 24 has conjugate (3,2,2,2,1,1) with product also 24.
The Heinz numbers of these partitions are given by A325040.
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LINKS
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EXAMPLE
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The a(8) = 6 through a(15) = 6 integer partitions:
(44) (333) (4321) (641) (4422) (4432) (6431)
(332) (51111) (52111) (4331) (53211) (6421) (8411)
(431) (322211) (621111) (53311) (54221)
(2222) (611111) (432211) (433211)
(3221) (7111111) (632111)
(4211) (7211111)
(42221111)
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MATHEMATICA
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conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Length[Select[IntegerPartitions[n], Times@@#==Times@@conj[#]&]], {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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