A326179 Number of subsets of {1..n} containing n whose product is divisible by their sum.

0, 1, 1, 2, 1, 5, 9, 15, 30, 65, 138, 274, 563, 1149, 2441, 5110, 9090, 19645, 37524, 79178, 156697, 324182, 663749, 1353984, 2529510, 5088926, 10686159, 19987129, 40800192, 85303150, 162549135, 341440697, 630392773, 1317158898, 2687152135, 5276362642, 10078384386, 21415439670, 43367751196, 86613992774, 166456115593

Offset: 0

Author

Gus Wiseman, Jun 13 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(7) = 15 subsets:
  {1}  {2}  {3}      {4}  {5}          {6}          {7}
            {1,2,3}       {1,4,5}      {3,6}        {1,6,7}
                          {2,3,5}      {2,4,6}      {2,5,7}
                          {3,4,5}      {4,5,6}      {3,4,7}
                          {1,2,3,4,5}  {1,2,3,6}    {3,5,7}
                                       {1,3,5,6}    {1,2,4,7}
                                       {3,4,5,6}    {2,3,6,7}
                                       {1,2,3,4,6}  {2,5,6,7}
                                       {2,3,4,5,6}  {3,5,6,7}
                                                    {1,2,5,6,7}
                                                    {1,3,4,5,7}
                                                    {1,3,4,6,7}
                                                    {2,3,4,5,7}
                                                    {2,4,5,6,7}
                                                    {1,2,3,4,5,6,7}
		

Crossrefs

Cf. A053632, A057567, A057568, A059529, A063865, A301987, A326153/A326154, A326156, A326158, A326178, A326180.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n],{1,n}],MemberQ[#,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 23 2019