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 A326643 Number of subsets of {1..n} whose mean and geometric mean are both integers. 11
 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 16, 17, 18, 19, 22, 23, 30, 31, 32, 33, 34, 35, 41, 46, 47, 70, 71, 72, 73, 74, 102, 103, 104, 105, 143, 144, 145, 146, 151, 152, 153, 154, 155, 161, 162, 163, 244, 252, 280, 281, 282, 283, 409, 410, 416, 417, 418, 419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS David Wasserman, Table of n, a(n) for n = 0..119 Wikipedia, Geometric mean EXAMPLE The a(1) = 1 through a(12) = 16 subsets: {1} {1} {1} {1} {1} {1} {1} {1} {1} {1} {1} {1} {2} {2} {2} {2} {2} {2} {2} {2} {2} {2} {2} {3} {3} {3} {3} {3} {3} {3} {3} {3} {3} {4} {4} {4} {4} {4} {4} {4} {4} {4} {5} {5} {5} {5} {5} {5} {5} {5} {6} {6} {6} {6} {6} {6} {6} {7} {7} {7} {7} {7} {7} {8} {8} {8} {8} {8} {2,8} {9} {9} {9} {9} {1,9} {10} {10} {10} {2,8} {1,9} {11} {11} {2,8} {1,9} {12} {2,8} {1,9} {2,8} {3,6,12} {3,4,9,12} MATHEMATICA Table[Length[Select[Subsets[Range[n]], IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 10}] CROSSREFS Partial sums of A326644. Subsets whose geometric mean is an integer are A326027. Subsets whose mean is an integer are A051293. Partitions with integer mean and geometric mean are A326641. Strict partitions with integer mean and geometric mean are A326029. Cf. A067538, A067539, A078175, A082553, A102627, A326623, A326625, A326645, A326646, A326647. Sequence in context: A234853 A060863 A063934 * A222030 A327261 A337133 Adjacent sequences: A326640 A326641 A326642 * A326644 A326645 A326646 KEYWORD nonn AUTHOR Gus Wiseman, Jul 16 2019 EXTENSIONS More terms from David Wasserman, Aug 03 2019 STATUS approved

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Last modified February 21 09:24 EST 2024. Contains 370228 sequences. (Running on oeis4.)