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A325853
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Number of integer partitions of n such that every pair of distinct parts has a different quotient.
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13
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1, 1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 69, 88, 116, 148, 193, 242, 309, 385, 484, 596, 746, 915, 1128, 1371, 1679, 2030, 2460, 2964, 3570, 4268, 5115, 6088, 7251, 8584, 10175, 12002, 14159, 16619, 19526, 22846, 26713, 31153, 36300, 42169, 48990, 56728
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OFFSET
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0,3
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COMMENTS
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Also the number of integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different product.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(7) = 14 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (321) (331)
(11111) (411) (511)
(2211) (2221)
(3111) (3211)
(21111) (4111)
(111111) (22111)
(31111)
(211111)
(1111111)
The one partition of 7 for which not every pair of distinct parts has a different quotient is (4,2,1).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@Divide@@@Subsets[Union[#], {2}]&]], {n, 0, 20}]
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CROSSREFS
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The integer partition case is A325853.
The strict integer partition case is A325854.
Heinz numbers of the counterexamples are given by A325994.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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