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A326489
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Number of product-free subsets of {1..n}.
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12
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1, 1, 2, 4, 6, 12, 22, 44, 88, 136, 252, 504, 896, 1792, 3392, 6352, 9720, 19440, 35664, 71328, 129952, 247232, 477664, 955328, 1700416, 2657280, 5184000, 10368000, 19407360, 38814720, 68868352, 137736704, 260693504, 505830400, 999641600, 1882820608, 2807196672
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OFFSET
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0,3
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COMMENTS
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A set is product-free if it contains no product of two (not necessarily distinct) elements.
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LINKS
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EXAMPLE
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The a(0) = 1 through a(6) = 22 subsets:
{} {} {} {} {} {} {}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{2,3} {4} {4} {4}
{2,3} {5} {5}
{3,4} {2,3} {6}
{2,5} {2,3}
{3,4} {2,5}
{3,5} {2,6}
{4,5} {3,4}
{2,3,5} {3,5}
{3,4,5} {3,6}
{4,5}
{4,6}
{5,6}
{2,3,5}
{2,5,6}
{3,4,5}
{3,4,6}
{3,5,6}
{4,5,6}
{3,4,5,6}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Intersection[#, Times@@@Tuples[#, 2]]=={}&]], {n, 10}]
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CROSSREFS
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Product-closed subsets are A326076.
Subsets containing no products are A326114.
Subsets containing no products of distinct elements are A326117.
Subsets containing no quotients are A327591.
Maximal product-free subsets are A326496.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(0)=1 prepended to data, example and b-file by Peter Kagey, Sep 18 2019
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STATUS
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approved
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