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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.
0
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.
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
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Jul 23 2022
STATUS
approved