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

Author

Gus Wiseman, Jun 11 2019

Keywords

• nonn

Examples

			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}
		

Crossrefs

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

Programs

Mathematica

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

Extensions

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

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