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

1,2

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.

Links

Table of n, a(n) for n=1..63.

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]

Crossrefs

Cf. A353187.

Sequence in context: A119356 A137582 A116965 * A306975 A123054 A093703

Adjacent sequences: A356004 A356005 A356006 * A356008 A356009 A356010

Keyword

nonn

Author

Ivan N. Ianakiev, Jul 23 2022

Status

approved