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

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%I A326180 #5 Jun 14 2019 21:52:14
%S A326180 0,1,1,1,1,1,3,1,1,1,11,1,16,1,1,1,27,1
%N A326180 Number of maximal subsets of {1..n} containing n whose product is divisible by their sum.
%F A326180 a(A060462(n)) = 1.
%e A326180 The a(6) = 3, a(10) = 11, and a(12) = 16 subsets:
%e A326180   {1,3,5,6}    {1,2,4,5,6,7,10}      {1,2,3,4,5,6,7,8,12}
%e A326180   {1,2,3,4,6}  {1,2,3,4,5,7,8,10}    {1,3,4,5,6,7,8,10,12}
%e A326180   {2,3,4,5,6}  {1,2,3,4,6,7,9,10}    {1,3,4,6,7,8,9,10,12}
%e A326180                {1,2,3,5,6,7,8,10}    {1,3,4,5,6,8,10,11,12}
%e A326180                {1,2,3,5,7,8,9,10}    {1,2,3,4,5,6,8,9,10,12}
%e A326180                {1,2,5,6,7,8,9,10}    {1,2,3,4,6,7,8,9,11,12}
%e A326180                {1,3,4,5,6,7,9,10}    {1,2,3,5,6,7,8,9,10,12}
%e A326180                {1,3,4,6,7,8,9,10}    {1,2,3,5,6,7,8,9,11,12}
%e A326180                {1,4,5,6,7,8,9,10}    {1,3,4,5,6,7,8,9,11,12}
%e A326180                {1,2,3,4,5,6,8,9,10}  {1,2,3,4,6,7,8,10,11,12}
%e A326180                {2,3,4,5,6,7,8,9,10}  {1,2,3,4,6,8,9,10,11,12}
%e A326180                                      {1,3,5,6,7,8,9,10,11,12}
%e A326180                                      {1,2,3,4,5,6,7,9,10,11,12}
%e A326180                                      {1,2,3,4,5,7,8,9,10,11,12}
%e A326180                                      {1,2,4,5,6,7,8,9,10,11,12}
%e A326180                                      {2,3,4,5,6,7,8,9,10,11,12}
%t A326180 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326180 Table[Length[fasmax[Select[Subsets[Range[n],{1,n}],MemberQ[#,n]&&Divisible[Times@@#,Plus@@#]&]]],{n,0,10}]
%Y A326180 Cf. A053632, A057567, A057568, A059529, A060462, A063865, A301987, A326153/A326154, A326156, A326158, A326178, A326179.
%K A326180 nonn,more
%O A326180 0,7
%A A326180 _Gus Wiseman_, Jun 13 2019