|
%I #11 Sep 18 2019 04:07:08
%S 1,1,2,2,3,4,5,7,9,10,16,22,27,39,52,70,90,120,150,198,262,357,448,
%T 602,782,1004,1294,1715,2229,2932,3698,4844,6259,8188,10274,13446,
%U 16895,21954,27470,35843,45411
%N Number of maximal subsets of {1..n} containing no differences or quotients of pairs of distinct elements.
%F a(n) = A326497(n) + 1 for n > 1. - _Andrew Howroyd_, Aug 30 2019
%e The a(1) = 1 through a(9) = 10 subsets:
%e {1} {1} {1} {1} {1} {1} {1} {1} {1}
%e {2} {2,3} {2,3} {2,3} {2,3} {2,3,7} {2,5,6} {2,6,7}
%e {3,4} {2,5} {2,5,6} {2,5,6} {2,5,8} {3,4,5}
%e {3,4,5} {3,4,5} {2,6,7} {2,6,7} {3,5,7}
%e {4,5,6} {3,4,5} {3,4,5} {2,3,7,8}
%e {3,5,7} {3,5,7} {2,5,6,9}
%e {4,5,6,7} {2,3,7,8} {2,5,8,9}
%e {4,5,6,7} {4,5,6,7}
%e {5,6,7,8} {4,6,7,9}
%e {5,6,7,8,9}
%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Union[Divide@@@Reverse/@Subsets[#,{2}],Subtract@@@Reverse/@Subsets[#,{2}]]]=={}&]]],{n,0,10}]
%Y Subsets without differences or quotients are A326490.
%Y Subsets with differences and quotients are A326494.
%Y Maximal subsets without differences are A121269
%Y Maximal subsets without quotients are A326492.
%Y Cf. A007865, A051026, A054519, A326023, A326117, A326489, A326496, A327591.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jul 09 2019
%E a(16)-a(40) from _Andrew Howroyd_, Aug 30 2019
|
