A096172 - OEIS

%I #29 Sep 02 2017 05:35:56

%S 2,17,41,257,313,1297,1201,241,193,137,7321,233,14281,937,1489,65537,

%T 41761,929,3833,160001,97241,3209,139921,331777,11489,26881,6481,

%U 614657,353641,3361,1129,61681,6113,1336337,750313,98801,10529,50857,1156721

%N Largest prime factor of n^4 + 1.

%C Mabkhout shows that a(n) >= 137 for n > 3. - _Charles R Greathouse IV_, Apr 07 2014

%D Mustapha Mabkhout, Minoration de P(x^4+1), Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari 63:2 (1993), pp. 135-148.

%H Vincenzo Librandi and T. D. Noe, <a href="/A096172/b096172.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)

%H Florian Luca, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AAPASM_31_from19to24.pdf">Primitive divisors of Lucas sequences and prime factors of x^2 + 1 and x^4 + 1</a>, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31 (2004).

%F a(n) = A006530(1+n^4) = A014442(n^2). - _R. J. Mathar_, Jan 28 2017

%e a(1)=2 because 1^4 + 1 = 2;

%e a(2)=17: 2^4 + 1 = 17;

%e a(8)=241: 8^4 + 1 = 4097 = 17*241.

%t FactorInteger[#^4+1][[-1,1]]&/@Range[40] (* _Harvey P. Dale_, Apr 30 2012 *)

%o (PARI) a(n)=my(f=factor(n^4+1)[,1]); f[#f] \\ _Charles R Greathouse IV_, Apr 07 2014

%Y Cf. A000068, A002523, A037896, A069170, A096169, A096171.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Jun 19 2004