A326156 Number of nonempty subsets of {1..n} whose product is divisible by their sum.

0, 1, 2, 4, 5, 10, 19, 34, 64, 129, 267, 541, 1104, 2253, 4694, 9804, 18894, 38539, 76063, 155241, 311938, 636120, 1299869, 2653853, 5183363, 10272289, 20958448, 40945577, 81745769, 167048919, 329598054, 671038751, 1301431524, 2618590422, 5305742557, 10582105199, 20660489585, 42075929255, 85443680451, 172057673225, 338513788818

Offset: 0

Author

Gus Wiseman, Jun 11 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(6) = 19 subsets:
  {1}  {1}  {1}      {1}      {1}          {1}
       {2}  {2}      {2}      {2}          {2}
            {3}      {3}      {3}          {3}
            {1,2,3}  {4}      {4}          {4}
                     {1,2,3}  {5}          {5}
                              {1,2,3}      {6}
                              {1,4,5}      {3,6}
                              {2,3,5}      {1,2,3}
                              {3,4,5}      {1,4,5}
                              {1,2,3,4,5}  {2,3,5}
                                           {2,4,6}
                                           {3,4,5}
                                           {4,5,6}
                                           {1,2,3,6}
                                           {1,3,5,6}
                                           {3,4,5,6}
                                           {1,2,3,4,5}
                                           {1,2,3,4,6}
                                           {2,3,4,5,6}
		

Links

• Bert Dobbelaere, C++ program

Crossrefs

Cf. A053632, A057567, A057568, A059529, A063865, A301987, A326150, A326151, A326153/A326154, A326155, A326158, A326178, A326179, A326180.

Programs

Mathematica

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

Extensions

a(21)-a(30) from Alois P. Heinz, Jun 13 2019

a(31)-a(40) from Bert Dobbelaere, Jun 22 2019