A219186 - OEIS

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.

%I #3 Nov 14 2012 01:02:17

%S 1,2,3,4,6,8,14,18,20,24,32,38,42,44,54,60,62,68,72,74,80,90,98,104,

%T 108,110,114,132,140,150,152,158,164,168,180,182,194,198,200,212,234,

%U 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

%N 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.

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

%C The sequence is infinite as proved by Baoulina and Luca.

%H I. Baoulina and F. Luca, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_35_from11to19.pdf">On positive integers with a certain nondivisibility property</a>, Annales Mathematicae et Informaticae 35 (2008), pp. 11-19.

%Y Cf. A164014

%K nonn

%O 1,2

%A _Max Alekseyev_, Nov 14 2012