cp's OEIS Frontend

A263022 a(n) = gcd(n, 1^(n-1) + 2^(n-1) + ... + (n-1)^(n-1)) for n > 1.

%I A263022 #36 Oct 08 2015 19:34:58
%S A263022 1,1,4,1,3,1,8,3,5,1,12,1,7,5,16,1,9,1,20,7,11,1,24,5,13,9,28,1,15,1,
%T A263022 32,11,17,35,36,1,19,13,40,1,21,1,44,3,23,1,48,7,25,17,52,1,27,55,56,
%U A263022 19,29,1,60,1,31,21,64,13,33,1,68,23,35,1,72,1,37,25,76,77,39,1,80,27,41,1,84,17,43,29,88,1,45,13,92,31,47,95,96
%N A263022 a(n) = gcd(n, 1^(n-1) + 2^(n-1) + ... + (n-1)^(n-1)) for n > 1.
%C A263022 a(n) = 1 if and only if n is a prime or n is a Carmichael number.
%C A263022 a(n) is divisible by 4 if n is divisible by 4, otherwise a(n) is odd. - _Robert Israel_, Oct 08 2015
%C A263022 a(n) = n iff 4|n or n = 35, 55, 77, 95; A121707 ?
%C A263022 a(5005) = 11: this is the first case where a(n) is prime and A001222(n) > 3. - _Altug Alkan_, Oct 08 2015
%H A263022 Robert Israel, <a href="/A263022/b263022.txt">Table of n, a(n) for n = 2..10000</a>
%F A263022 a(4n) = 4n.
%F A263022 a(n) = gcd(A031971(n-1), n). - _Michel Marcus_, Oct 08 2015
%p A263022 f:= n -> igcd(n, add(j &^(n-1) mod n, j=1..n-1)):
%p A263022 seq(f(n), n=2..1000); # _Robert Israel_, Oct 08 2015
%t A263022 Table[GCD[n, Total@ Map[#^(n - 1) &, Range[n - 1]]], {n, 2, 96}] (* _Michael De Vlieger_, Oct 08 2015 *)
%o A263022 (PARI) vector(100, n, gcd(n+1, sum(k=1, n, k^n))) \\ _Altug Alkan_, Oct 08 2015
%Y A263022 Cf. A002997 (see my Oct 09 2013 comment).
%K A263022 nonn
%O A263022 2,3
%A A263022 _Thomas Ordowski_, Oct 07 2015