This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060385 #58 Jan 05 2025 19:51:36
%S A060385 2,3,5,2,13,7,17,11,89,3,233,29,61,47,1597,19,113,41,421,199,28657,23,
%T A060385 3001,521,109,281,514229,61,2417,2207,19801,3571,141961,107,2221,9349,
%U A060385 135721,2161,59369,421,433494437,307,109441,28657,2971215073,1103
%N A060385 Largest prime factor of n-th Fibonacci number.
%C A060385 For n > 12, Fibonacci(n) is divisible by a primitive prime factor (one not dividing Fibonacci(1), ..., Fibonacci(n-1)). But all primes up to n-2 divide smaller Fibonacci numbers, see A001602, so a(n) >= n-1 for n > 12. This strengthens a more general theorem of Bravo and Luca. - _Charles R Greathouse IV_, Feb 01 2013
%H A060385 Tyler Busby, <a href="/A060385/b060385.txt">Table of n, a(n) for n = 3..1422</a> (terms 3..1000 from Charles R Greathouse IV, terms 1001..1408 from Amiram Eldar)
%H A060385 U. Alfred, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/1-1/alfred2.pdf">On the form of primitive factors of Fibonacci numbers</a>, Fibonacci Quarterly 1:1 (1963), pp. 43-45.
%H A060385 Jhon J. Bravo and Florian Luca, <a href="http://arxiv.org/abs/1210.4101">On the largest prime factor of the k-Fibonacci numbers</a>, arXiv:1210.4101 [math.NT], 2012.
%H A060385 D. E. Daykin and L. A. G. Dresel, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/8-1/daykin-a.pdf">Factorization of Fibonacci numbers</a>, Fibonacci Quarterly 8:1 (1970), pp. 23-30.
%F A060385 a(n) >= n - 1 for n > 12, see comments. It is not hard to show that a(n) > 1000 for n > 88. Similarly a(n) > 20641 for n > 120. - _Charles R Greathouse IV_, Feb 01 2013
%e A060385 F(82) = 2789 * 59369 * 370248451, so a(82) = 370248451.
%t A060385 Table[First[Last[FactorInteger[Fibonacci[n]]]], {n, 3, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 03 2012 *)
%o A060385 (PARI) a(n)=my(f=factor(fibonacci(n))[,1]);f[#f] \\ _Charles R Greathouse IV_, Feb 01 2013
%o A060385 (Magma) [Maximum(PrimeDivisors(Fibonacci(n))): n in [3..50]]; // _Vincenzo Librandi_, Dec 25 2016
%Y A060385 Cf. A000045, A022307, A001605, A060319, A060320, A051694, A193615.
%K A060385 nonn
%O A060385 3,1
%A A060385 _Labos Elemer_, Apr 03 2001