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A326023
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Number of subsets of {1..n} containing all of their integer quotients.
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19
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1, 2, 3, 5, 9, 17, 25, 49, 73, 145, 217, 433, 553, 1105, 1657, 2593, 3937, 7873, 10057, 20113, 26689, 42321, 63481, 126961, 154801, 309601, 464401, 737569, 992161, 1984321, 2450881, 4901761, 6292801, 10197313, 15295969, 26241697, 32947489, 65894977, 98842465, 161587873, 205842529
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OFFSET
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0,2
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COMMENTS
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These are sets that are closed under taking the quotient of two (not necessarily distinct) divisible terms.
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(5) = 17 subsets:
{} {} {} {} {} {}
{1} {1} {1} {1} {1}
{1,2} {1,2} {1,2} {1,2}
{1,3} {1,3} {1,3}
{1,2,3} {1,4} {1,4}
{1,2,3} {1,5}
{1,2,4} {1,2,3}
{1,3,4} {1,2,4}
{1,2,3,4} {1,2,5}
{1,3,4}
{1,3,5}
{1,4,5}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Divide@@@Tuples[#, 2], IntegerQ]]&]], {n, 0, 10}]
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CROSSREFS
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Cf. A007865, A051026, A054519, A067992, A103580, A325853, A325854, A325860, A325861, A325994, A326078.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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