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 A356007 #4 Aug 24 2022 09:53:24
%S A356007 1,2,3,4,5,6,9,10,11,16,17,18,64,65,66,81,82,83,100,101,102,121,122,
%T A356007 123,144,145,146,169,170,173,196,197,199,225,226,227,256,257,258,289,
%U A356007 290,291,324,326,327,361,362,365,400,401,402,441,442,443,484,485,487,529,530,533,576,577,579
%N A356007 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair whose numbers of divisors are not coprime.
%C A356007 For every k>=0, every (3k+1)-th term is square, because a triple of terms with {odd,even,even} number of divisors must be followed by a similar triple.
%t A356007 coQ[n_,m_]:=CoprimeQ[DivisorSigma[0,n],DivisorSigma[0,m]];
%t A356007 f[x_,y_,z_]:=Sort[{coQ[x,y],coQ[x,z],coQ[y,z]}];
%t A356007 next[n_,m_]:=Module[{k=m+1},While[f[n,m,k]!={False,True,True},k++];k];
%t A356007 a[1]=1;a[2]=2;a[n_]:=a[n]=next[a[n-2],a[n-1]];a/@Range[102]
%Y A356007 Cf. A353187.
%K A356007 nonn
%O A356007 1,2
%A A356007 _Ivan N. Ianakiev_, Jul 23 2022