A326179 - OEIS

%I #16 Jun 23 2019 02:47:29

%S 0,1,1,2,1,5,9,15,30,65,138,274,563,1149,2441,5110,9090,19645,37524,

%T 79178,156697,324182,663749,1353984,2529510,5088926,10686159,19987129,

%U 40800192,85303150,162549135,341440697,630392773,1317158898,2687152135,5276362642,10078384386,21415439670,43367751196,86613992774,166456115593

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

%e The a(1) = 1 through a(7) = 15 subsets:

%e   {1}  {2}  {3}      {4}  {5}          {6}          {7}

%e             {1,2,3}       {1,4,5}      {3,6}        {1,6,7}

%e                           {2,3,5}      {2,4,6}      {2,5,7}

%e                           {3,4,5}      {4,5,6}      {3,4,7}

%e                           {1,2,3,4,5}  {1,2,3,6}    {3,5,7}

%e                                        {1,3,5,6}    {1,2,4,7}

%e                                        {3,4,5,6}    {2,3,6,7}

%e                                        {1,2,3,4,6}  {2,5,6,7}

%e                                        {2,3,4,5,6}  {3,5,6,7}

%e                                                     {1,2,5,6,7}

%e                                                     {1,3,4,5,7}

%e                                                     {1,3,4,6,7}

%e                                                     {2,3,4,5,7}

%e                                                     {2,4,5,6,7}

%e                                                     {1,2,3,4,5,6,7}

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

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

%K nonn

%O 0,4

%A _Gus Wiseman_, Jun 13 2019

%E a(21)-a(30) from _Alois P. Heinz_, Jun 13 2019

%E a(31)-a(40) from _Bert Dobbelaere_, Jun 23 2019