This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326494 #8 Aug 25 2019 19:45:12
%S A326494 1,2,4,6,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,
%T A326494 49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,
%U A326494 95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127
%N A326494 Number of subsets of {1..n} containing all differences and quotients of pairs of distinct elements.
%C A326494 The only allowed sets are the empty set, any singleton, any initial interval of positive integers and {2,4}. This can be shown by induction. - _Andrew Howroyd_, Aug 25 2019
%F A326494 a(n) = 2*n + 1 = A005408(n) for n > 3. - _Andrew Howroyd_, Aug 25 2019
%e A326494 The a(0) = 1 through a(6) = 13 subsets:
%e A326494 {} {} {} {} {} {} {}
%e A326494 {1} {1} {1} {1} {1} {1}
%e A326494 {2} {2} {2} {2} {2}
%e A326494 {1,2} {3} {3} {3} {3}
%e A326494 {1,2} {4} {4} {4}
%e A326494 {1,2,3} {1,2} {5} {5}
%e A326494 {2,4} {1,2} {6}
%e A326494 {1,2,3} {2,4} {1,2}
%e A326494 {1,2,3,4} {1,2,3} {2,4}
%e A326494 {1,2,3,4} {1,2,3}
%e A326494 {1,2,3,4,5} {1,2,3,4}
%e A326494 {1,2,3,4,5}
%e A326494 {1,2,3,4,5,6}
%t A326494 Table[Length[Select[Subsets[Range[n]],SubsetQ[#,Union[Divide@@@Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&],Subtract@@@Select[Tuples[#,2],Greater@@#&]]]&]],{n,0,10}]
%Y A326494 Subsets with difference are A054519.
%Y A326494 Subsets with quotients are A326023.
%Y A326494 Subsets with quotients > 1 are A326079.
%Y A326494 Subsets without differences or quotients are A326490.
%Y A326494 Cf. A005408, A007865, A051026, A325849, A326076, A326491.
%K A326494 nonn
%O A326494 0,2
%A A326494 _Gus Wiseman_, Jul 09 2019
%E A326494 Terms a(20) and beyond from _Andrew Howroyd_, Aug 25 2019