A055386 Smallest factor of (2n)^(2n) + 1.

5, 257, 13, 97, 101, 89, 29, 274177, 5, 148721, 5, 17, 53, 449, 17, 641, 13, 17, 5, 17, 5, 41, 29, 769, 41, 89, 13, 17, 5, 17, 5, 59649589127497217, 37, 41, 13, 97, 149, 17, 5, 15361, 5, 1753, 13, 17, 41, 449, 1129, 1153, 5, 17, 5, 1201, 17, 1777, 89, 4993, 41

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

			8^8 + 1 = 97 * 257 * 673, so a(4) = 97.
		

References

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..313
• Is there any value of n other than 1, 2 and 4, such that n^n+1 is a prime?

Crossrefs

Cf. A014566, A055385.

Programs

Mathematica

Table[With[{k = 2 n}, FactorInteger[k^k + 1]][[1, 1]], {n, 1, 60, 1}] (* Vincenzo Librandi, Jul 23 2013 *)

PARI

a(n) = factor((2*n)^(2*n) + 1)[1, 1] \\ Michel Marcus, Jul 23 2013; corrected by Jason Yuen, Jun 01 2025

Formula

a(n) = A055385(2*n). - Michel Marcus, Jul 23 2013