The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #8 Sep 13 2017 00:02:19
%S 1,1,4,3,2,44,1,24,28,319,14,168,1,2204,16,231,2,15124,1,1584,4,
%T 103679,2,4176,7,710644,56,28623,2,4870844,1,150024,4,33385279,2,
%U 205656,101,228826124,256,269247,14,1568397604,49,9227232,4,10749957119,2,24157728,1
%N a(n) = gcd(Sum_{k=1...n} L(k), Product_{j=1...n} L(j)), where L(k) is the k-th Lucas number.
%C Observation: For k = 1,2,... the numbers L(4k)-3 = 4, 44, 319, 2204, 15124, 103679, 710644, 4870844, 33385279,... are in the sequence.
%e The first 6 Lucas numbers are 1, 3, 4, 7, 11, 18 => 1+3+4+7+11+18 = 44. So a(6) = gcd(44, 1*3*4*7*11*18) = 44.
%p with(combinat,fibonacci):a:=n->2*fibonacci(n-1)+fibonacci(n): seq(gcd(add(a(i), i=1..n), mul(a(j), j=1..n)), n=1..50);
%t nn=60; With[{prs=LucasL[Range[nn]]}, Table[GCD[Total[Take[prs, n]], Times@@Take[ prs, n]], {n, nn}]]
%Y Cf. A000204, A239740.
%K nonn
%O 1,3
%A _Michel Lagneau_, Mar 27 2014