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A326079 Number of subsets of {1..n} containing all of their integer quotients > 1.

%I A326079 #8 Aug 30 2019 21:47:29
%S A326079 1,2,4,8,16,32,48,96,144,288,432,864,1104,2208,3312,5184,7872,15744,
%T A326079 20112,40224,53376,84640,126960,253920,309600,619200,928800,1475136,
%U A326079 1984320,3968640,4901760,9803520,12585600,20394624,30591936,52483392,65894976,131789952,197684928,323175744,411685056
%N A326079 Number of subsets of {1..n} containing all of their integer quotients > 1.
%C A326079 These sets are closed under taking the quotient of two distinct divisible terms.
%F A326079 For n > 0, a(n) = 2 * A326078(n) = 2 * (A326023(n) - 1).
%e A326079 The a(6) = 48 subsets:
%e A326079   {}  {1}  {1,2}  {1,2,3}  {1,2,3,4}  {1,2,3,4,5}  {1,2,3,4,5,6}
%e A326079       {2}  {1,3}  {1,2,4}  {1,2,3,5}  {1,2,3,4,6}
%e A326079       {3}  {1,4}  {1,2,5}  {1,2,3,6}  {1,2,3,5,6}
%e A326079       {4}  {1,5}  {1,3,4}  {1,2,4,5}  {2,3,4,5,6}
%e A326079       {5}  {1,6}  {1,3,5}  {1,3,4,5}
%e A326079       {6}  {2,3}  {1,4,5}  {1,4,5,6}
%e A326079            {2,4}  {1,4,6}  {2,3,4,5}
%e A326079            {2,5}  {1,5,6}  {2,3,4,6}
%e A326079            {3,4}  {2,3,4}  {2,3,5,6}
%e A326079            {3,5}  {2,3,5}
%e A326079            {4,5}  {2,3,6}
%e A326079            {4,6}  {2,4,5}
%e A326079            {5,6}  {3,4,5}
%e A326079                   {4,5,6}
%t A326079 Table[Length[Select[Subsets[Range[n]],SubsetQ[#,Divide@@@Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]]&]],{n,0,10}]
%Y A326079 Cf. A007865, A051026, A054519, A067992, A103580, A325860, A325994, A326023, A326076, A326078, A326081.
%K A326079 nonn
%O A326079 0,2
%A A326079 _Gus Wiseman_, Jun 05 2019
%E A326079 Terms a(21) and beyond from _Andrew Howroyd_, Aug 30 2019