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A319318
Number of integer partitions of n such that every distinct submultiset has a different GCD.
11
1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 2, 6, 5, 5, 5, 8, 5, 9, 6, 8, 9, 11, 6, 11, 11, 11, 10, 14, 9, 16, 12, 14, 15, 15, 11, 19, 17, 17, 14, 22, 15, 22, 18, 18, 21, 25, 16, 24, 21, 23, 22, 28, 21, 26, 22, 26, 27, 32, 20, 35, 30, 27, 27, 31, 27, 38, 30, 33, 29
OFFSET
1,5
COMMENTS
Note that such partitions are necessarily strict.
EXAMPLE
The a(31) = 16 partitions are (31), (16,15), (17,14), (18,13), (19,12), (20,11), (21,10), (22,9), (23,8), (24,7), (25,6), (26,5), (27,4), (28,3), (29,2), (15,10,6).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@GCD@@@Union[Rest[Subsets[#]]]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2018
STATUS
approved