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A326027 Number of subsets of {1..n} whose geometric mean is an integer. 18
0, 1, 2, 3, 6, 7, 8, 9, 12, 19, 20, 21, 28, 29, 30, 31, 40, 41, 70, 71, 74, 75, 76, 77, 108, 123, 124, 211, 214, 215, 216, 217, 332, 333, 334, 335, 592, 593, 594, 595, 612, 613, 614, 615, 618, 639, 640, 641, 1160, 1183, 1324, 1325, 1328, 1329, 2176, 2177, 2196 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..56.

Wikipedia, Geometric mean

EXAMPLE

The a(1) = 1 through a(9) = 19 subsets:

  {1}  {1}  {1}  {1}      {1}      {1}      {1}      {1}      {1}

       {2}  {2}  {2}      {2}      {2}      {2}      {2}      {2}

            {3}  {3}      {3}      {3}      {3}      {3}      {3}

                 {4}      {4}      {4}      {4}      {4}      {4}

                 {1,4}    {5}      {5}      {5}      {5}      {5}

                 {1,2,4}  {1,4}    {6}      {6}      {6}      {6}

                          {1,2,4}  {1,4}    {7}      {7}      {7}

                                   {1,2,4}  {1,4}    {8}      {8}

                                            {1,2,4}  {1,4}    {9}

                                                     {2,8}    {1,4}

                                                     {1,2,4}  {1,9}

                                                     {2,4,8}  {2,8}

                                                              {4,9}

                                                              {1,2,4}

                                                              {1,3,9}

                                                              {2,4,8}

                                                              {3,8,9}

                                                              {4,6,9}

                                                              {3,6,8,9}

MATHEMATICA

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

CROSSREFS

First differences are A082553.

Partitions whose geometric mean is an integer are A067539.

Strict partitions whose geometric mean is an integer are A326625.

Subsets whose average is an integer are A051293.

Cf. A078174, A078175, A102627, A326567/A326568, A326622, A326623, A326624.

Sequence in context: A275884 A003605 A132188 * A255527 A316156 A319737

Adjacent sequences:  A326024 A326025 A326026 * A326028 A326029 A326030

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 14 2019

STATUS

approved

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Last modified March 3 13:15 EST 2021. Contains 341762 sequences. (Running on oeis4.)