A187025 a(n) is the least number k such that k*n+1 is a prime dividing n^n-1.

1, 4, 1, 2, 1, 4, 2, 2, 1, 1436, 1, 4, 501969, 4, 1, 644, 1, 5784852794328402307380, 2, 2, 1, 20, 3, 4, 36, 4, 1, 2, 1, 18353950678197027912484562396837972855962080, 8, 2, 3, 8, 1, 4, 5, 4, 1, 2, 1, 4, 2, 4, 1, 36, 2, 4, 3, 128, 1, 2, 5, 85840, 2, 4, 1, 12, 1, 16, 273

Offset: 2

Author

Michel Lagneau, Mar 02 2011

Keywords

• nonn

Comments

The smallest prime factor of n^n-1 of the form k*n+1 is A187023(n).

Examples

			7^7-1 = 2*3*29*4733; the smallest prime divisor of the form k*n+1 is 29 = 4*7+1, hence a(7) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..138

Crossrefs

Cf. A187023, A187024.

Programs

Magma

A187025:=function(n); for d in PrimeDivisors(n^n-1) do if d mod n eq 1 then return (d-1)/n; end if; end for; return 0; end function; [ A187025(n): n in [2..50] ]; // Klaus Brockhaus, Mar 02 2011

Mathematica

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