A055385 Smallest prime factor of n^n + 1.

2, 5, 2, 257, 2, 13, 2, 97, 2, 101, 2, 89, 2, 29, 2, 274177, 2, 5, 2, 148721, 2, 5, 2, 17, 2, 53, 2, 449, 2, 17, 2, 641, 2, 13, 2, 17, 2, 5, 2, 17, 2, 5, 2, 41, 2, 29, 2, 769, 2, 41, 2, 89, 2, 13, 2, 17, 2, 5, 2, 17, 2, 5, 2, 59649589127497217, 2, 37, 2, 41, 2, 13, 2, 97, 2, 149

Offset: 1

Author

Walter Nissen, Jun 24 2000

Keywords

• nonn

Comments

If we use the commonly accepted convention that 0^0 = 1, then a(0) = 2. - Chai Wah Wu, Jul 22 2019

Examples

			4^4 + 1 = 257 prime, so a(4) = 257;
6^6 + 1 = 13 * 37 * 97, so a(6) = 13.
		

References

• C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988. Page 82.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A014566, A055386.

Programs

Mathematica

Table[FactorInteger[n^n + 1][[1, 1]], {n, 74}] (* Vincenzo Librandi, Jul 23 2013 *)

PARI

a(n) = {if (n % 2, return (2)); return (factor(n^n + 1)[1, 1]);} \\ Michel Marcus, Jul 23 2013