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A239799
a(n) = gcd(Sum_{k=1...n} L(k), Product_{j=1...n} L(j)), where L(k) is the k-th Lucas number.
0
1, 1, 4, 3, 2, 44, 1, 24, 28, 319, 14, 168, 1, 2204, 16, 231, 2, 15124, 1, 1584, 4, 103679, 2, 4176, 7, 710644, 56, 28623, 2, 4870844, 1, 150024, 4, 33385279, 2, 205656, 101, 228826124, 256, 269247, 14, 1568397604, 49, 9227232, 4, 10749957119, 2, 24157728, 1
OFFSET
1,3
COMMENTS
Observation: For k = 1,2,... the numbers L(4k)-3 = 4, 44, 319, 2204, 15124, 103679, 710644, 4870844, 33385279,... are in the sequence.
EXAMPLE
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.
MAPLE
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);
MATHEMATICA
nn=60; With[{prs=LucasL[Range[nn]]}, Table[GCD[Total[Take[prs, n]], Times@@Take[ prs, n]], {n, nn}]]
CROSSREFS
Sequence in context: A245348 A174551 A349811 * A305235 A120011 A177924
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 27 2014
STATUS
approved