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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
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.
Sequence in context: A234853 A060863 A063934 * A222030 A327261 A337133
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.)