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%I #18 Jul 22 2018 12:31:37
%S 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,
%T 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,
%U 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
%N a(n) = gcd(n! + 1, n^n + 1).
%C 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).
%C From _Antti Karttunen_, Jul 22 2018: (Start)
%C The first duplicated value > 1 is 157519 = a(43755) = a(78759). Note that 43755 = 15*2917, while 78759 = 27*2917.
%C 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.
%C (End)
%H Antti Karttunen, <a href="/A116891/b116891.txt">Table of n, a(n) for n = 1..80001</a>
%e a(3) = gcd(3! + 1, 3^3 + 1) = gcd(7,28) = 7.
%t Table[GCD[n! + 1, n^n + 1], {n, 101}] (* _Robert G. Wilson v_, Mar 09 2006 *)
%o (PARI) A116891(n) = gcd(n!+1,(n^n)+1); \\ _Antti Karttunen_, Jul 22 2018
%Y Cf. A014566, A038507, A067658, A116892, A116893, A116894.
%K easy,nonn
%O 1,1
%A _Giovanni Resta_, Mar 01 2006
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