

A190781


Lucas Aurifeuillian primitive part B of Lucas(10*n  5).


2



11, 31, 151, 911, 541, 3641, 272611, 18451, 12760031, 7947701, 767131, 4106261531, 28144128251, 34379101, 120196353941, 823837075741, 51164521, 4215154433351, 2918000731816531, 73998076231, 12462174208709101, 939587136717207031, 3467131047901
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OFFSET

1,1


LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..250
John Brillhart, Peter L. Montgomery and Robert D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), pp. 251260, S1.
C. K. Caldwell, "Top Twenty" page, Lucas Aurifeuillian primitive part


FORMULA

a(n) = GCD(A061447(10*n5), A032908(n)*A106729(n1) + 1).


MATHEMATICA

lst = {1}; n = 23; Do[f = LucasL[k]; Do[f = f/GCD[f, lst[[d]]], {d, Most@Divisors[k]}]; AppendTo[lst, f], {k, 2, 10*n  5}]; Table[GCD[lst[[5*k]], 5*Fibonacci[k]*(Fibonacci[k] + 1) + 1], {k, 1, 2*n  1, 2}]


CROSSREFS

Cf. A061447, A190757.
Sequence in context: A181150 A094622 A193645 * A001604 A144727 A002535
Adjacent sequences: A190778 A190779 A190780 * A190782 A190783 A190784


KEYWORD

nonn


AUTHOR

Arkadiusz Wesolowski, Dec 29 2012


STATUS

approved



