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%I #18 Dec 11 2024 15:03:59
%S 3,1,1,1,33,1,1,1,513,1,1,1,8193,1,1,1,131073,1,1,1,2097153,1,1,1,
%T 33554433,1,1,1,536870913,1,1,1,8589934593,1,1,1,137438953473,1,1,1,
%U 2199023255553,1,1,1,35184372088833,1,1,1,562949953421313,1,1,1
%N a(n) = gcd(2^((n*(n+1)/2)) + 1, 2^n + 1).
%H Harry J. Smith, <a href="/A066827/b066827.txt">Table of n, a(n) for n = 1..500</a>
%F If n is not congruent to 1 mod 4, a(n) = 1. If n is congruent to 1 mod 4, a(n) = 2^n + 1.
%F G.f.: (-16x^5-2x^2+3x)/(16x^4-1)/(x-1). - _Ralf Stephan_, Mar 12 2003
%t Table[If[Mod[n,4]==1,2^n+1,1],{n,80}] (* _Harvey P. Dale_, Jun 30 2022 *)
%o (PARI) a(n) = { gcd(2^((n*(n+1)/2)) + 1, 2^n + 1) } \\ _Harry J. Smith_, Mar 30 2010
%K nonn
%O 1,1
%A _Benoit Cloitre_, Jan 20 2002