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

0,9

Links

Table of n, a(n) for n=0..119.

Wikipedia, Geometric mean

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.

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

Sequence in context: A079692 A110269 A238280 * A120964 A318810 A319989

Adjacent sequences: A326641 A326642 A326643 * A326645 A326646 A326647

Keyword

nonn

Author

Gus Wiseman, Jul 16 2019

Extensions

More terms from David Wasserman, Aug 03 2019

Status

approved