A190757 Lucas Aurifeuillian primitive part A of Lucas(10*n - 5).

1, 1, 101, 71, 181, 39161, 24571, 12301, 1158551, 87382901, 21211, 373270451, 28143378001, 32414581, 1322154751061, 9062194370461, 1550853481, 2819407321151, 265272771839851, 2366632711, 137083914639998701, 85417012034751151, 3455782010101

Offset

1,3

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. 251-260, S1.

C. K. Caldwell, "Top Twenty" page, Lucas Aurifeuillian primitive part

Formula

a(n) = GCD(A061447(10*n-5), A027941(n-1)*A106729(n-1) + 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, A190781.

Sequence in context: A269503 A067748 A338615 * A212603 A278584 A282066

Adjacent sequences: A190754 A190755 A190756 * A190758 A190759 A190760

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 29 2012

Status

approved