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 A327466 #19 Oct 03 2019 21:41:49
%S A327466 1,1,3,4,8,13,19,23,27,36,46,55,67,80,94,103,119,132,150,167,187,208,
%T A327466 230,250,266,291,311,336,364,393,423,447,479,512,546
%N A327466 Number of nonempty subsets of [1..n] which are geometric progressions with rational ratio and are locally maximal.
%C A327466 "Locally maximal" subsets are those subsets in geometrical progression that cannot be extended to a larger subset of [1..n] in geometric progression. [Comment made precise by _Giovanni Resta_, Sep 30 2019.]
%C A327466 One might have expected that the GP would be required to have an integer ratio, but in fact we allow rational ratios. The GPs can be assumed to be strictly increasing. - _N. J. A. Sloane_, Oct 03 2019
%e A327466 Illustrations of some initial terms:
%e A327466 n=3: (12),(13),(23).
%e A327466 n=4: (124),(13),(23),(34).
%e A327466 n=8: (1248), plus all 28 pairs (ij) from [1..8] except the six subsets of (1248), so a(8) = 1 + 28 - 6 = 23.
%t A327466 a[1] = 1; a[n_] := Block[{t = Select[ Subsets[ Range[n], {2, Ceiling[ Log2[n + 1]]}], Length@ Union[ Rest[#]/ Most[#]] == 1 &], i = 2}, t = Reverse@ SortBy[t, Length]; i=2; While[i <= Length[t], If[ AnyTrue[ Take[t, i-1], SubsetQ[#, t[[i]]] &], t = Delete[t, i]; i=2; Continue[], i++]]; Length@ t]; Array[a, 16] (* _Giovanni Resta_, Sep 30 2019 *)
%Y A327466 See A327469 for GPs of length > 2.
%Y A327466 Cf. A309095.
%K A327466 nonn,more
%O A327466 1,3
%A A327466 _N. J. A. Sloane_, Sep 29 2019
%E A327466 a(9)-a(35) from _Giovanni Resta_, Sep 30 2019