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.

1, 2, 3, 4, 5, 6, 9, 10, 11, 16, 17, 18, 64, 65, 66, 81, 82, 83, 100, 101, 102, 121, 122, 123, 144, 145, 146, 169, 170, 173, 196, 197, 199, 225, 226, 227, 256, 257, 258, 289, 290, 291, 324, 326, 327, 361, 362, 365, 400, 401, 402, 441, 442, 443, 484, 485, 487, 529, 530, 533, 576, 577, 579

Offset: 1

Author

Ivan N. Ianakiev, Jul 23 2022

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A353187.

Programs

Mathematica

coQ[n_,m_]:=CoprimeQ[DivisorSigma[0,n],DivisorSigma[0,m]];
f[x_,y_,z_]:=Sort[{coQ[x,y],coQ[x,z],coQ[y,z]}];
next[n_,m_]:=Module[{k=m+1},While[f[n,m,k]!={False,True,True},k++];k];
a[1]=1;a[2]=2;a[n_]:=a[n]=next[a[n-2],a[n-1]];a/@Range[102]