A116891 a(n) = gcd(n! + 1, n^n + 1).

2, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 79, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 103, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 191, 1, 1, 1, 199, 1, 1

Offset: 1

Author

Giovanni Resta, Mar 01 2006

Keywords

• easy
• nonn

Comments

Apparently all the values greater than 1 (cf. A116892) are prime numbers and are equal to 2n+1 with only 4 exceptions for n<82000 (cf. A116894).

From Antti Karttunen, Jul 22 2018: (Start)

The first duplicated value > 1 is 157519 = a(43755) = a(78759). Note that 43755 = 15*2917, while 78759 = 27*2917.

It seems that for the long time after a(1) = 2, all other terms > 1 occur only at such positions k that k+1 is not squarefree. However, this turns out to be false as a(208161) = 555097, and 208162 is a squarefree number.

(End)

Examples

			a(3) = gcd(3! + 1, 3^3 + 1) = gcd(7,28) = 7.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..80001

Crossrefs

Cf. A014566, A038507, A067658, A116892, A116893, A116894.

Programs

Mathematica

Table[GCD[n! + 1, n^n + 1], {n, 101}] (* Robert G. Wilson v, Mar 09 2006 *)

PARI

A116891(n) = gcd(n!+1,(n^n)+1); \\ Antti Karttunen, Jul 22 2018