login
A326644
Number of subsets of {1..n} containing n whose mean and geometric mean are both integers.
7
0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 1, 6, 5, 1, 23, 1, 1, 1, 1, 28, 1, 1, 1, 38, 1, 1, 1, 5, 1, 1, 1, 1, 6, 1, 1, 81, 8, 28, 1, 1, 1, 126, 1, 6, 1, 1, 1, 37, 1, 1, 6, 208, 1, 1, 1, 1, 1, 1, 1, 351, 1, 1, 381, 1, 1, 1, 1, 159, 605, 1, 1, 9, 1, 1, 1, 2, 1, 1223, 1, 1, 1, 1, 1, 805, 1, 113, 2, 5021, 1, 1, 1, 2, 1, 1, 1, 2630, 1, 1, 1, 54, 1, 1, 1, 1, 2, 1, 1
OFFSET
0,9
EXAMPLE
The a(1) = 1 through a(12) = 3 subsets:
{1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12}
{2,8} {1,9} {3,6,12}
{3,4,9,12}
The a(18) = 7 subsets:
{18}
{2,18}
{8,18}
{1,8,9,18}
{2,3,8,9,18}
{6,12,16,18}
{2,3,4,9,12,18}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 10}]
CROSSREFS
First differences of A326643.
Subsets whose mean is an integer are A051293.
Subsets whose geometric mean is an integer are A326027.
Partitions with integer mean and geometric mean are A326641.
Strict partitions with integer mean and geometric mean are A326029.
Sequence in context: A079692 A110269 A238280 * A120964 A318810 A319989
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2019
EXTENSIONS
More terms from David Wasserman, Aug 03 2019
STATUS
approved