A116892 Values of gcd(k!+1, k^k+1), when greater than 1.

2, 7, 47, 79, 103, 127, 191, 199, 263, 367, 383, 431, 479, 503, 599, 607, 631, 727, 743, 823, 839, 863, 887, 991, 1087, 1151, 1319, 1367, 1423, 1487, 1511, 1583, 1663, 1783, 1823, 1871, 1951, 2039, 2063, 2111, 2143, 2287, 2311, 2383, 2423, 2447, 2503, 2551

Offset: 1

Author

Giovanni Resta, Mar 01 2006

Keywords

• easy
• nonn

Comments

Apart from the initial term (2) and few exceptional values (A116894) this sequence seems to coincide with A067658. The values of k for which the terms of this sequence are obtained are in A116893.

Examples

			gcd(1!+1,1^1+1) = 2 gives the first term;
gcd(3!+1,3^3+1) = gcd(7,28) = 7 gives the second, and so on.
		

Links

• Nick Hobson, Table of n, a(n) for n = 1..10000 (first 1832 terms from Antti Karttunen)

Crossrefs

Cf. A014566, A038507, A067658, A116891, A116893, A116894.

Programs

C

See Links section in A116893.

Mathematica

f[n_] := GCD[n! + 1, n^n + 1]; t = Array[f, 1295]; Rest@ Union@ t (* Robert G. Wilson v, Mar 09 2006 *)

PARI

lista(nn) = for (n=1, nn, if ((g=gcd(n! + 1, n^n + 1)) != 1, print1(g, ", "))); \\ Michel Marcus, Jul 22 2018

Extensions

Entries checked by Robert G. Wilson v, Mar 09 2006