A326643 Number of subsets of {1..n} whose mean and geometric mean are both integers.

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

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