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%I #21 May 11 2021 10:34:49
%S 2,1,3,1,7,11,1,29,47,19,41,199,23,521,281,31,2207,3571,107,9349,2161,
%T 211,43,139,1103,101,90481,5779,14503,59,2521,3010349,1087,9901,67,71,
%U 103681,54018521,29134601,79,1601,370248451,83,6709,263,181,4969
%N Smallest primitive prime factor of the n-th Lucas number (A000032); i.e., L(n), L(0) = 2, L(1) = 1 and L(n) = L(n-1) + L(n-2).
%C A Lucas number can have more than one primitive factor; the primitive factors of L(22) are 43 and 307.
%H T. D. Noe, <a href="/A058036/b058036.txt">Table of n, a(n) for n = 0..1000</a> (using Blair Kelly's data).
%H Mansur S. Boase, <a href="https://www.fq.math.ca/Scanned/39-5/boase.pdf">A Result About the Primes Dividing Fibonacci Numbers</a>, The Fibonacci Quarterly, 39.5 (2001) 386.
%H J. Brillhart, P. L. Montgomery and R. D. Silverman, <a href="https://doi.org/10.1090/S0025-5718-1988-0917832-6">Tables of Fibonacci and Lucas factorizations</a>, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
%H Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>
%t a=3; b=-1; prms={}; Table[c=a+b; a=b; b=c; f=First/@FactorInteger[c]; p=Complement[f, prms]; prms=Join[prms, p]; If[p=={}, 1, First[p]], {47}]
%o (PARI) lucas(n) = fibonacci(n+1)+fibonacci(n-1); \\ A000032
%o a(n) = {n++; my(v = vector(n, k, k--; lucas(k))); my(vf = vector(n, k, factor(v[k])[,1]~)); for (k=1, n-1, vf[n] = setminus(vf[n], vf[k]);); if (#vf[n], vecmin(vf[n]), 1);} \\ _Michel Marcus_, May 11 2021
%Y Cf. A000032, A086600 (number of primitive prime factors in L(n)).
%Y Cf. A001578 (analog for Fibonacci).
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Nov 16 2000
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