A326644 Number of subsets of {1..n} containing n whose mean and geometric mean are both integers.

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

Author

Gus Wiseman, Jul 16 2019

Keywords

• nonn

Examples

			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}
		

Links

• Wikipedia, Geometric mean

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.

Cf. A067538, A067539, A082550, A082553, A102627, A326028, A326623, A326625, A326645, A326647.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]],{n,0,10}]

Extensions

More terms from David Wasserman, Aug 03 2019