A116894 Numbers k such that gcd(k! + 1, k^k + 1) is neither 1 nor 2k+1.

1, 5427, 41255, 43755, 208161, 496175, 497135

Offset: 1

Author

Giovanni Resta, Mar 01 2006

Keywords

• nonn
• hard
• more

Comments

g(n) = gcd(n! + 1, n^n + 1) is almost always equal to 1 or to 2n+1. These are the known exceptions: g(1) = 2, g(5427) = 10453, g(41255) = 129341, g(43755) = 157519, g(208161) = 555097. - Hans Havermann, Mar 28 2006

a(8) > 1000000. - Nick Hobson, Feb 20 2024

Examples

			gcd(1! + 1, 1^1 + 1) = 2 and 2 != 2*1 + 1, so 1 belongs to the sequence.
		

Crossrefs

Cf. A014566, A038507, A067658, A116891, A116892, A116893.

Programs

C

// See Links section in A116893.

Extensions

a(5) from Hans Havermann, Mar 28 2006

a(6)-a(7) from Nick Hobson, Feb 20 2024