%I #25 Feb 20 2024 08:23:04

%S 2,7,47,79,103,127,191,199,263,367,383,431,479,503,599,607,631,727,

%T 743,823,839,863,887,991,1087,1151,1319,1367,1423,1487,1511,1583,1663,

%U 1783,1823,1871,1951,2039,2063,2111,2143,2287,2311,2383,2423,2447,2503,2551

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

%C 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.

%H Nick Hobson, <a href="/A116892/b116892.txt">Table of n, a(n) for n = 1..10000</a> (first 1832 terms from Antti Karttunen)

%e gcd(1!+1,1^1+1) = 2 gives the first term;

%e gcd(3!+1,3^3+1) = gcd(7,28) = 7 gives the second, and so on.

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

%o (PARI) lista(nn) = for (n=1, nn, if ((g=gcd(n! + 1, n^n + 1)) != 1, print1(g, ", "))); \\ _Michel Marcus_, Jul 22 2018

%o (C) See Links section in A116893.

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

%K easy,nonn

%O 1,1

%A _Giovanni Resta_, Mar 01 2006

%E Entries checked by _Robert G. Wilson v_, Mar 09 2006