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A370587
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Number of subsets of {1..n} containing n such that it is not possible to choose a different prime factor of each element (non-choosable).
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13
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0, 1, 1, 2, 6, 10, 24, 44, 116, 236, 468, 908, 1960, 3776, 7812, 15876, 32504, 63744, 130104
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(0) = 0 through a(5) = 10 subsets:
. {1} {1,2} {1,3} {1,4} {1,5}
{1,2,3} {2,4} {1,2,5}
{1,2,4} {1,3,5}
{1,3,4} {1,4,5}
{2,3,4} {2,4,5}
{1,2,3,4} {1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], MemberQ[#, n] && Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]], {n, 0, 10}]
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CROSSREFS
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The complement is counted by A370586.
For a unique choice we have A370588.
For binary indices instead of factors we have A370639, complement A370589.
A355741 counts choices of a prime factor of each prime index.
A368098 counts choosable unlabeled multiset partitions, complement A368097.
A370585 counts maximal choosable sets.
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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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