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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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. Cf. A002033, A103300, A108917, A143823, A196724, A325768, A325856, A325868, A325869, A325876. Sequence in context: A035968 A112581 A288255 * A035976 A035985 A035995 Adjacent sequences:  A325850 A325851 A325852 * A325854 A325855 A325856 KEYWORD nonn AUTHOR Gus Wiseman, May 31 2019 STATUS approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)