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

1,1

Comments

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A014566, A055386.

Sequence in context: A170908 A229029 A379544 * A160503 A108429 A130280

Adjacent sequences: A055382 A055383 A055384 * A055386 A055387 A055388

Keyword

nonn

Author

Walter Nissen, Jun 24 2000

Status

approved