

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
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OFFSET

0,3


LINKS



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

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.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



