|
%I #15 Apr 03 2023 10:36:12
%S 1,1,101,71,181,39161,24571,12301,1158551,87382901,21211,373270451,
%T 28143378001,32414581,1322154751061,9062194370461,1550853481,
%U 2819407321151,265272771839851,2366632711,137083914639998701,85417012034751151,3455782010101
%N Lucas Aurifeuillian primitive part A of Lucas(10*n - 5).
%H Arkadiusz Wesolowski, <a href="/A190757/b190757.txt">Table of n, a(n) for n = 1..250</a>
%H John Brillhart, Peter L. Montgomery and Robert D. Silverman, <a href="http://www.ams.org/journals/mcom/1988-50-181/S0025-5718-1988-0917832-6/">Tables of Fibonacci and Lucas factorizations</a>, Math. Comp. 50 (1988), pp. 251-260, S1.
%H C. K. Caldwell, "Top Twenty" page, <a href="https://t5k.org/top20/page.php?id=21">Lucas Aurifeuillian primitive part</a>
%F a(n) = GCD(A061447(10*n-5), A027941(n-1)*A106729(n-1) + 1).
%t 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}]
%Y Cf. A061447, A190781.
%K nonn
%O 1,3
%A _Arkadiusz Wesolowski_, Dec 29 2012
|
