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