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A370590
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Number of maximal subsets of {1..n} containing n such that it is possible to choose a different prime factor of each element (choosable).
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3
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0, 0, 1, 1, 1, 2, 3, 5, 2, 4, 14, 25, 13, 38, 46, 66, 28, 178, 57
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OFFSET
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0,6
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COMMENTS
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For example, the set {4,7,9,10} has choice (2,7,3,5) so is counted under a(10).
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LINKS
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EXAMPLE
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The a(0) = 0 through a(10) = 14 subsets (A = 10):
. . 2 23 34 235 256 2357 3578 2579 237A
345 356 2567 5678 4579 267A
456 3457 5679 279A
3567 5789 347A
4567 357A
367A
378A
467A
479A
567A
579A
678A
679A
789A
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n], {PrimePi[n]}], MemberQ[#, n]&&Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]>0&]], {n, 0, 10}]
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CROSSREFS
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A355741 counts choices of a prime factor of each prime index.
A368098 counts choosable unlabeled multiset partitions, complement A368097.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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