A326172 Number of nonempty subsets of {2..n} whose product is divisible by their sum.

0, 0, 1, 2, 3, 6, 12, 21, 34, 69, 140, 278, 561, 1144, 2367, 4936, 9503, 19368, 38202, 77911, 156458, 318911, 651462, 1329624, 2596458, 5144833, 10494839, 20500025, 40923643, 83620258, 164982516, 335873558, 651383048, 1310551707, 2655240565, 5295397093, 10338145110, 21052407259, 42748787713, 86078893923, 169349494068

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Example

The a(2) = 1 through a(7) = 21 subsets:
  {2}  {2}  {2}  {2}      {2}          {2}
       {3}  {3}  {3}      {3}          {3}
            {4}  {4}      {4}          {4}
                 {5}      {5}          {5}
                 {2,3,5}  {6}          {6}
                 {3,4,5}  {3,6}        {7}
                          {2,3,5}      {3,6}
                          {2,4,6}      {2,3,5}
                          {3,4,5}      {2,4,6}
                          {4,5,6}      {2,5,7}
                          {3,4,5,6}    {3,4,5}
                          {2,3,4,5,6}  {3,4,7}
                                       {3,5,7}
                                       {4,5,6}
                                       {2,3,6,7}
                                       {2,5,6,7}
                                       {3,4,5,6}
                                       {3,5,6,7}
                                       {2,3,4,5,6}
                                       {2,3,4,5,7}
                                       {2,4,5,6,7}

Mathematica

Table[Length[Select[Subsets[Range[2, n], {1, n}], Divisible[Times@@#, Plus@@#]&]], {n, 0, 10}]

Crossrefs

Cf. A053632, A057567, A057568, A059529, A063865, A301987, A325037, A325044, A326150, A326151, A326153/A326154, A326155, A326156, A326158, A326178.

Sequence in context: A227940 A382328 A081156 * A082877 A047090 A185265

Adjacent sequences: A326169 A326170 A326171 * A326173 A326174 A326175

Keyword

nonn

Author

Gus Wiseman, Jun 11 2019

Extensions

a(21)-a(29) from Alois P. Heinz, Jun 13 2019

a(30)-a(40) from Bert Dobbelaere, Jun 22 2019

Status

approved