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A325855
Number of strict integer partitions of n such that every pair of distinct parts has a different product.
10
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 14, 18, 22, 25, 31, 37, 44, 53, 59, 69, 83, 100, 111, 129, 152, 173, 198, 232, 260, 302, 342, 386, 448, 498, 565, 646, 728, 819, 918, 1039, 1164, 1310, 1462, 1631, 1830, 2053, 2282, 2532, 2825, 3136, 3482, 3869, 4300, 4744
OFFSET
0,4
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..250
EXAMPLE
The a(1) = 1 through a(10) = 10 partitions (A = 10):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
(21) (31) (32) (42) (43) (53) (54) (64)
(41) (51) (52) (62) (63) (73)
(321) (61) (71) (72) (82)
(421) (431) (81) (91)
(521) (432) (532)
(531) (541)
(621) (631)
(721)
(4321)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Times@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]
CROSSREFS
The subset case is A196724.
The maximal case is A325859.
The integer partition case is A325856.
The strict integer partition case is A325855.
Heinz numbers of the counterexamples are given by A325993.
Sequence in context: A034141 A055002 A114097 * A174246 A083847 A034142
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved