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A079451 Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.

%I A079451 #48 Aug 06 2025 08:51:54
%S A079451 2,1,3,2,7,11,3,29,47,19,41,199,23,521,281,31,2207,3571,107,9349,2161,
%T A079451 211,307,461,1103,151,90481,5779,14503,19489,2521,3010349,4481,9901,
%U A079451 63443,911,103681,54018521,29134601,859,3041,370248451,1427,144481,967,541,275449
%N A079451 Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.
%H A079451 Amiram Eldar, <a href="/A079451/b079451.txt">Table of n, a(n) for n = 0..1000</a> (using Blair Kelly's data)
%H A079451 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 A079451 Blair Kelly, <a href="https://mersennus.net/fibonacci/l1000.txt">Factorizations of first 1000 Lucas numbers.</a>
%F A079451 a(n) = A006530(A000032(n)). - _Felix Fröhlich_, Dec 26 2016
%p A079451 A079451 := proc(n)
%p A079451         A006530(A000032(n)) ;
%p A079451 end proc:
%p A079451 seq(A079451(n),n=0..30) ; # _R. J. Mathar_, Oct 26 2013
%p A079451 # second Maple program:
%p A079451 a:= n-> max(ifactors((<<1|1>, <1|0>>^n. <<2, -1>>)[1, 1])[2][..., 1][], 1):
%p A079451 seq(a(n), n=0..46);  # _Alois P. Heinz_, Aug 04 2025
%t A079451 Join[{2,1},f[n_]:=(FactorInteger@LucasL@n)[[-1,1]];Array[f,60,2]] (* _Vincenzo Librandi_, Dec 26 2016 *)
%o A079451 (PARI) a(n) = my(f = factor(fibonacci(n+1)+fibonacci(n-1))); if (om = #f~, f[om, 1], 1); \\ _Michel Marcus_, Oct 26 2013
%o A079451 (PARI) A079451(n) = A006530(A000032(n)) \\ _M. F. Hasler_, Apr 10 2025
%o A079451 (Magma) [2,1] cat [Maximum(PrimeDivisors(Lucas(n))): n in [2..60]]; // _Vincenzo Librandi_, Dec 26 2016
%o A079451 (Python)
%o A079451 def A079451(n): return A006530(A000032(n)) # _M. F. Hasler_, Apr 10 2025
%Y A079451 Cf. A000032 (Lucas numbers), A006530 (greatest prime factor).
%Y A079451 Cf. A001606 (indices of prime Lucas numbers <=> where a(n) = A000032(n)), subsequence of A076697 (indices of record values in this sequence).
%Y A079451 Cf. A280104 (same for smallest prime factor).
%K A079451 nonn
%O A079451 0,1
%A A079451 _Lekraj Beedassy_, Jan 13 2003
%E A079451 More terms from _Michel Marcus_, Oct 26 2013
%E A079451 Modified b-file and scripts so that a(1)=1. - _David Radcliffe_, Aug 03 2025