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A326027
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Number of subsets of {1..n} whose geometric mean is an integer.
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28
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0, 1, 2, 3, 6, 7, 8, 9, 12, 19, 20, 21, 28, 29, 30, 31, 40, 41, 70, 71, 74, 75, 76, 77, 108, 123, 124, 211, 214, 215, 216, 217, 332, 333, 334, 335, 592, 593, 594, 595, 612, 613, 614, 615, 618, 639, 640, 641, 1160, 1183, 1324, 1325, 1328, 1329, 2176, 2177, 2196
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The a(1) = 1 through a(9) = 19 subsets:
{1} {1} {1} {1} {1} {1} {1} {1} {1}
{2} {2} {2} {2} {2} {2} {2} {2}
{3} {3} {3} {3} {3} {3} {3}
{4} {4} {4} {4} {4} {4}
{1,4} {5} {5} {5} {5} {5}
{1,2,4} {1,4} {6} {6} {6} {6}
{1,2,4} {1,4} {7} {7} {7}
{1,2,4} {1,4} {8} {8}
{1,2,4} {1,4} {9}
{2,8} {1,4}
{1,2,4} {1,9}
{2,4,8} {2,8}
{4,9}
{1,2,4}
{1,3,9}
{2,4,8}
{3,8,9}
{4,6,9}
{3,6,8,9}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], IntegerQ[GeometricMean[#]]&]], {n, 0, 10}]
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CROSSREFS
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Partitions whose geometric mean is an integer are A067539.
Strict partitions whose geometric mean is an integer are A326625.
Subsets whose average is an integer are A051293.
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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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