A187022 a(n) is the smallest prime factor of n^n+1 having the form k*n+1.

5, 7, 257, 521, 13, 113, 97, 73, 101, 23, 193, 13417, 29, 31, 274177, 45957792327018709121, 37, 108301, 148721, 337, 9617835527609, 47, 33409, 239201, 53, 163, 449, 233, 61, 373, 641, 661, 6009977, 71, 22452257707354557235348829785471057921, 593, 202921, 79, 641

Offset: 2

Author

Michel Lagneau, Mar 02 2011

Keywords

• nonn

Comments

The values of k are in A187024.

Examples

			12^12+1 = 89*193*233*2227777; the smallest prime divisor of the form k*n+1 is 193 = 16*12+1, hence a(12) = 193.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..148 (terms 2..100 from Vincenzo Librandi)

Crossrefs

Cf. A187024.

Programs

Magma

A187022:=function(n); for d in PrimeDivisors(n^n+1) do if d mod n eq 1 then return d; end if; end for; return 0; end function; [ A187022(n): n in [2..40] ]; // Klaus Brockhaus, Mar 02 2011

Mathematica

Table[p=First/@FactorInteger[n^n+1]; Select[p, Mod[#1, n] == 1 &, 1][[1]], {n, 2, 40}]