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 A123273 #12 Oct 26 2019 21:59:50
%S A123273 1,1,2,3,4,4,4,5,6,6,6,6,6,6,6,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,10,
%T A123273 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
%U A123273 10,10,10,10,10,10,10,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12
%N A123273 a(0) = 1; a(n) = the number of earlier terms, a(k), where gcd(a(k), a(floor(k/2))) = 1.
%e A123273 Among terms a(0) through a(8) (1,1,2,3,4,4,4,5,6), a(0) is coprime to a(0), a(1) is coprime to a(0), a(2) is coprime to a(1), a(3) is coprime to a(1), a(6) is coprime to a(3) and a(7) is coprime to a(3). There are 6 such coprime pairs in the range, so a(9) = 6.
%t A123273 f[l_List] := Append[l, Count[Table[GCD[l[[k]], l[[Floor[(k + 1)/2]]]], {k, Length[l]}], 1]];Nest[f, {1}, 80] (* _Ray Chandler_, Oct 17 2006 *)
%K A123273 nonn
%O A123273 0,3
%A A123273 _Leroy Quet_, Oct 10 2006
%E A123273 Extended by _Ray Chandler_, Oct 17 2006