A219186 Positive integers n such that 1+(k-2)*U_m(k,1)^2 does not divide n-k for any 3<=k<n and m>=1, where U(k,1) is a Lucas sequence.

1, 2, 3, 4, 6, 8, 14, 18, 20, 24, 32, 38, 42, 44, 54, 60, 62, 68, 72, 74, 80, 90, 98, 104, 108, 110, 114, 132, 140, 150, 152, 158, 164, 168, 180, 182, 194, 198, 200, 212, 234, 240, 242, 258, 270, 272, 278, 284, 294, 308, 312, 332, 338, 348, 350, 360, 368, 374, 380, 384, 398, 402, 410, 420, 422, 432, 434, 440, 450, 458, 464

Offset

1,2

Comments

Related to solubility of generalized Markov equation x_1^2 + x_2^2 + ... + x_n^2 = k*x_1*x_2*...*x_n.

The sequence is infinite as proved by Baoulina and Luca.

Links

Table of n, a(n) for n=1..71.

I. Baoulina and F. Luca, On positive integers with a certain nondivisibility property, Annales Mathematicae et Informaticae 35 (2008), pp. 11-19.

Crossrefs

Cf. A164014

Sequence in context: A018137 A084239 A283022 * A049708 A000031 A298072

Adjacent sequences: A219183 A219184 A219185 * A219187 A219188 A219189

Keyword

nonn

Author

Max Alekseyev, Nov 14 2012

Status

approved