OFFSET
1,1
COMMENTS
a(n) = 0 for n = 39, 60, 69, 72, ... .
a(5385) has 1126 decimal digits. - Chai Wah Wu, Nov 19 2020
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..5384 (n = 1..1000 from Alois P. Heinz)
EXAMPLE
a(6) = 13 because F(6)^2 + 1 = 8^2 + 1 = 65 = 5*13 and 13 is the greatest prime Fibonacci divisor.
MAPLE
a:= proc(n) local F, m, t; F, m, t:=
[1, 2], 0, (<<0|1>, <1|1>>^n)[2, 1]^2+1;
while F[2]<=t do if isprime(F[2]) and irem(t, F[2])=0
then m:=F[2] fi; F:= [F[2], F[1]+F[2]]
od; m
end:
seq(a(n), n=1..50); # Alois P. Heinz, Nov 07 2020
PROG
(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
a(n) = my(f=factor(fibonacci(n)^2+1)[, 1]~, v=select(x->isfib(x), f)); if (#v, vecmax(v), 0); \\ Michel Marcus, Nov 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 07 2020
STATUS
approved