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%I #9 Feb 15 2020 22:17:18
%S 1,1,1,2,1,1,3,1,1,19,41,1,7,1,281,11,1,1,3,1,2161,29,43,461,47,101,
%T 90481,19,14503,19489,3,1,4481,199,67,29,7,1,29134601,79,1601,1,3,
%U 144481,263,11,4969,1,769,599786069,41,919,103,1,3,199,10745088481,229
%N Second-smallest prime factor of the n-th Lucas number (beginning with 2), if composite, or 1 otherwise.
%e a(3) = 2 because the 3rd of the Lucas numbers (beginning at 2) is A000032(3) = 4 = 2^2, hence depending on whether one means by second-smallest prime factor (i.e., distinct or not, with multiplicity or not) a(3) would be either 2 or 1.
%e a(10) is unambiguously 41, because L(10) = 123 = 3 * 41, and 41 is the second-smallest prime factor, with no issues of multiplicity or distinctness.
%t Table[f = FactorInteger[LucasL[n]]; If[Length[f] > 1, f[[2, 1]], If[Length[f] == 1 && f[[1, 2]] > 1, f[[1, 1]], 1]], {n, 0, 70}] (* _T. D. Noe_, Aug 15 2011 *)
%Y Cf. A000032, A000040, A001606, A005479, A193615.
%K nonn,easy
%O 0,4
%A _Jonathan Vos Post_, Aug 14 2011
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