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A326115 Number of maximal double-free subsets of {1..n}.

%I A326115 #10 Jun 15 2019 10:40:57
%S A326115 1,1,2,2,2,2,4,4,6,6,12,12,12,12,24,24,32,32,64,64,64,64,128,128,192,
%T A326115 192,384,384,384,384,768,768,960,960,1920,1920,1920,1920,3840,3840,
%U A326115 5760,5760,11520,11520,11520,11520,23040,23040,30720,30720
%N A326115 Number of maximal double-free subsets of {1..n}.
%C A326115 A set is double-free if no element is twice any other element.
%H A326115 Charlie Neder, <a href="/A326115/b326115.txt">Table of n, a(n) for n = 0..1000</a>
%F A326115 From _Charlie Neder_, Jun 11 2019: (Start)
%F A326115 a(n) = Product {k < n/2} A000931(8+floor(log_2(n/(2k+1)))).
%F A326115 a(2k+1) = a(2k), a(8k+4) = a(8k+3). (End)
%e A326115 The a(1) = 1 through a(9) = 6 sets:
%e A326115   {1}  {1}  {13}  {23}   {235}   {235}   {2357}   {13457}  {134579}
%e A326115        {2}  {23}  {134}  {1345}  {256}   {2567}   {13578}  {135789}
%e A326115                                  {1345}  {13457}  {14567}  {145679}
%e A326115                                  {1456}  {14567}  {15678}  {156789}
%e A326115                                                   {23578}  {235789}
%e A326115                                                   {25678}  {256789}
%t A326115 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326115 Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,2*#]=={}&]]],{n,0,10}]
%Y A326115 Cf. A000931, A007865, A050291, A103580, A120641, A308546, A320340, A323092.
%Y A326115 Cf. A325865, A326020, A326022, A326083.
%K A326115 nonn
%O A326115 0,3
%A A326115 _Gus Wiseman_, Jun 06 2019
%E A326115 a(16)-a(49) from _Charlie Neder_, Jun 11 2019