A079451 - OEIS

%I #29 Sep 08 2022 08:45:08

%S 2,0,3,2,7,11,3,29,47,19,41,199,23,521,281,31,2207,3571,107,9349,2161,

%T 211,307,461,1103,151,90481,5779,14503,19489,2521,3010349,4481,9901,

%U 63443,911,103681,54018521,29134601,859,3041,370248451,1427,144481,967,541

%N Highest prime dividing the n-th Lucas number (A000032); 0 when no such prime exists.

%H Amiram Eldar, <a href="/A079451/b079451.txt">Table of n, a(n) for n = 0..1000</a> (using Blair Kelly's data)

%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//l1000.txt">Factorizations of first 1000 Lucas numbers.</a>

%F a(n) = A006530(A000032(n)). - _Felix Fröhlich_, Dec 26 2016

%p A079451 := proc(n)

%p     if n = 1 then

%p         0;

%p     else

%p         A006530(A000032(n)) ;

%p     end if;

%p end proc:

%p seq(A079451(n),n=0..30) ; # _R. J. Mathar_, Oct 26 2013

%t Join[{2,0},f[n_]:=(FactorInteger@LucasL@n)[[-1,1]];Array[f,60,2]] (* _Vincenzo Librandi_, Dec 26 2016 *)

%o (PARI) a(n) = my(f = factor(fibonacci(n+1)+fibonacci(n-1))); if (om = #f~, f[om, 1], 0); \\ _Michel Marcus_, Oct 26 2013

%o (Magma) [2,0] cat [Maximum(PrimeDivisors(Lucas(n))): n in [2..60]]; // _Vincenzo Librandi_, Dec 26 2016

%Y Cf. A000032, A006530.

%K nonn

%O 0,1

%A _Lekraj Beedassy_, Jan 13 2003

%E More terms from _Michel Marcus_, Oct 26 2013