A326180 Number of maximal subsets of {1..n} containing n whose product is divisible by their sum.

0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 1, 16, 1, 1, 1, 27, 1

Offset: 0

Author

Gus Wiseman, Jun 13 2019

Keywords

• nonn
• more

Examples

			The a(6) = 3, a(10) = 11, and a(12) = 16 subsets:
  {1,3,5,6}    {1,2,4,5,6,7,10}      {1,2,3,4,5,6,7,8,12}
  {1,2,3,4,6}  {1,2,3,4,5,7,8,10}    {1,3,4,5,6,7,8,10,12}
  {2,3,4,5,6}  {1,2,3,4,6,7,9,10}    {1,3,4,6,7,8,9,10,12}
               {1,2,3,5,6,7,8,10}    {1,3,4,5,6,8,10,11,12}
               {1,2,3,5,7,8,9,10}    {1,2,3,4,5,6,8,9,10,12}
               {1,2,5,6,7,8,9,10}    {1,2,3,4,6,7,8,9,11,12}
               {1,3,4,5,6,7,9,10}    {1,2,3,5,6,7,8,9,10,12}
               {1,3,4,6,7,8,9,10}    {1,2,3,5,6,7,8,9,11,12}
               {1,4,5,6,7,8,9,10}    {1,3,4,5,6,7,8,9,11,12}
               {1,2,3,4,5,6,8,9,10}  {1,2,3,4,6,7,8,10,11,12}
               {2,3,4,5,6,7,8,9,10}  {1,2,3,4,6,8,9,10,11,12}
                                     {1,3,5,6,7,8,9,10,11,12}
                                     {1,2,3,4,5,6,7,9,10,11,12}
                                     {1,2,3,4,5,7,8,9,10,11,12}
                                     {1,2,4,5,6,7,8,9,10,11,12}
                                     {2,3,4,5,6,7,8,9,10,11,12}
		

Crossrefs

Cf. A053632, A057567, A057568, A059529, A060462, A063865, A301987, A326153/A326154, A326156, A326158, A326178, A326179.

Programs

Mathematica

fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n],{1,n}],MemberQ[#,n]&&Divisible[Times@@#,Plus@@#]&]]],{n,0,10}]

Formula

a(A060462(n)) = 1.