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Primitive part of Lucas(n).
10

%I #19 Apr 03 2023 10:36:10

%S 1,3,4,7,11,6,29,47,19,41,199,46,521,281,31,2207,3571,321,9349,2161,

%T 211,13201,64079,2206,15251,90481,5779,101521,1149851,2521,3010349,

%U 4870847,9901,4250681,64681,103681,54018521,29134601,67861,4868641,370248451

%N Primitive part of Lucas(n).

%H T. D. Noe, <a href="/A061447/b061447.txt">Table of n, a(n) for n=1..1000</a>

%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 C. K. Caldwell, <a href="https://t5k.org/top20/page.php?id=21">Lucas Aurifeuillian primitive part</a>

%F Primitive part of L(n) is primitive part of F(2n).

%F a(n) = Product_{ d divides 2*n } Fibonacci(2*n/d)^mu(d). - _Vladeta Jovovic_, Mar 08 2004

%t t={1}; Do[f=LucasL[n]; Do[f=f/GCD[f,t[[d]]], {d,Most[Divisors[n]]}]; AppendTo[t,f], {n,2,100}]; t

%Y Cf. A061446, A061254, A061445, A061442, A061443.

%Y Cf. A126015

%K nonn

%O 1,2

%A _David Broadhurst_, Jun 10 2001

%E More terms from _Vladeta Jovovic_, Mar 08 2004