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%I #4 Aug 24 2022 09:53:24
%S 1,2,3,4,5,6,9,10,11,16,17,18,64,65,66,81,82,83,100,101,102,121,122,
%T 123,144,145,146,169,170,173,196,197,199,225,226,227,256,257,258,289,
%U 290,291,324,326,327,361,362,365,400,401,402,441,442,443,484,485,487,529,530,533,576,577,579
%N 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 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 coQ[n_,m_]:=CoprimeQ[DivisorSigma[0,n],DivisorSigma[0,m]];
%t f[x_,y_,z_]:=Sort[{coQ[x,y],coQ[x,z],coQ[y,z]}];
%t next[n_,m_]:=Module[{k=m+1},While[f[n,m,k]!={False,True,True},k++];k];
%t a[1]=1;a[2]=2;a[n_]:=a[n]=next[a[n-2],a[n-1]];a/@Range[102]
%Y Cf. A353187.
%K nonn
%O 1,2
%A _Ivan N. Ianakiev_, Jul 23 2022
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