A061447 Primitive part of Lucas(n).

1, 3, 4, 7, 11, 6, 29, 47, 19, 41, 199, 46, 521, 281, 31, 2207, 3571, 321, 9349, 2161, 211, 13201, 64079, 2206, 15251, 90481, 5779, 101521, 1149851, 2521, 3010349, 4870847, 9901, 4250681, 64681, 103681, 54018521, 29134601, 67861, 4868641, 370248451

Offset: 1

Author

David Broadhurst, Jun 10 2001

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
• C. K. Caldwell, Lucas Aurifeuillian primitive part

Crossrefs

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

Cf. A126015

Programs

Mathematica

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

Formula

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

a(n) = Product_{ d divides 2*n } Fibonacci(2*n/d)^mu(d). - Vladeta Jovovic, Mar 08 2004

Extensions

More terms from Vladeta Jovovic, Mar 08 2004