A239799 - OEIS

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.

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

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=1..49.

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

Cf. A000204, A239740.

Sequence in context: A245348 A174551 A349811 * A305235 A120011 A177924

Adjacent sequences: A239796 A239797 A239798 * A239800 A239801 A239802

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 27 2014

STATUS

approved