A125258 Smallest prime divisor of n^4-n^2+1.

13, 73, 241, 601, 13, 13, 37, 6481, 9901, 13, 20593, 28393, 37, 13, 97, 83233, 229, 13, 13, 61, 157, 37, 13, 390001, 181, 530713, 13, 37, 809101, 922561, 13, 13, 1069, 277, 1678321, 13, 2083693, 2311921, 61, 13, 673, 3416953, 1753, 13, 13, 1213, 5306113

Offset

2,1

Comments

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

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

References

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

Links

Nick Hobson, Table of n, a(n) for n = 2..1000

Example

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

Mathematica

Table[FactorInteger[n^4-n^2+1][[1, 1]], {n, 2, 50}] (* Harvey P. Dale, Feb 27 2012 *)

Prog

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

Crossrefs

Cf. A060886, A124990.

Sequence in context: A142787 A084218 A175361 * A060886 A081586 A143008

Adjacent sequences: A125255 A125256 A125257 * A125259 A125260 A125261

Keyword

easy,nonn

Author

Nick Hobson, Nov 26 2006

Status

approved