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A319318
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Number of integer partitions of n such that every distinct submultiset has a different GCD.
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11
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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
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OFFSET
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1,5
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COMMENTS
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Note that such partitions are necessarily strict.
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@GCD@@@Union[Rest[Subsets[#]]]&]], {n, 30}]
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CROSSREFS
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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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