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A371128
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Number of strict integer partitions of n containing all distinct divisors of all parts.
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17
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1, 1, 0, 1, 1, 0, 2, 1, 2, 1, 2, 2, 3, 3, 3, 5, 3, 5, 6, 7, 7, 8, 8, 9, 12, 13, 13, 14, 15, 16, 19, 23, 25, 26, 26, 27, 36, 37, 40, 42, 46, 50, 55, 66, 65, 71, 71, 82, 90, 102, 103, 114, 117, 130, 147, 154, 166, 176, 182, 194, 228, 239, 259, 267, 287, 307, 336
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OFFSET
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0,7
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COMMENTS
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Also strict integer partitions such that the number of parts is equal to the number of distinct divisors of all parts.
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LINKS
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EXAMPLE
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The a(9) = 1 through a(19) = 7 partitions (A..H = 10..17):
531 721 731 B1 751 D1 B31 D21 B51 H1 B71
4321 5321 5421 931 B21 7521 7531 D31 9531 D51
6321 7321 7421 8421 64321 B321 A521 B521
9321 65321 B421 D321
54321 74321 75321 75421
84321 76321
94321
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&SubsetQ[#, Union@@Divisors/@#]&]], {n, 0, 30}]
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CROSSREFS
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A008284 counts partitions by length.
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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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