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A325853
Number of integer partitions of n such that every pair of distinct parts has a different quotient.
13
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
OFFSET
0,3
COMMENTS
Also the number of integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different product.
EXAMPLE
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).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@Divide@@@Subsets[Union[#], {2}]&]], {n, 0, 20}]
CROSSREFS
The subset case is A325860.
The maximal case is A325861.
The integer partition case is A325853.
The strict integer partition case is A325854.
Heinz numbers of the counterexamples are given by A325994.
Sequence in context: A035968 A112581 A288255 * A035976 A035985 A035995
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved