A125258 - OEIS

%I #11 Feb 11 2024 13:18:19

%S 13,73,241,601,13,13,37,6481,9901,13,20593,28393,37,13,97,83233,229,

%T 13,13,61,157,37,13,390001,181,530713,13,37,809101,922561,13,13,1069,

%U 277,1678321,13,2083693,2311921,61,13,673,3416953,1753,13,13,1213,5306113

%N Smallest prime divisor of n^4-n^2+1.

%C All divisors of n^4-n^2+1 are congruent to 1 modulo 12.

%C a(n) = 13 if and only if n is congruent to 2, -2, 6, or -6 modulo 13.

%D K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, NY, Second Edition (1990), p. 63.

%H Nick Hobson, <a href="/A125258/b125258.txt">Table of n, a(n) for n = 2..1000</a>

%e The prime divisors of 6^4-6^2+1=1261 are 13 and 97, so a(5) = 13.

%t Table[FactorInteger[n^4-n^2+1][[1,1]],{n,2,50}] (* _Harvey P. Dale_, Feb 27 2012 *)

%o (PARI) vector(49, n, if(n<2, "-", factor(n^4-n^2+1)[1,1]))

%Y Cf. A060886, A124990.

%K easy,nonn

%O 2,1

%A _Nick Hobson_, Nov 26 2006