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A213244 Number of nonzero elements in GF(2^n) that are 5th powers.

%I A213244 #32 Jan 11 2025 10:55:02
%S A213244 1,3,7,3,31,63,127,51,511,1023,2047,819,8191,16383,32767,13107,131071,
%T A213244 262143,524287,209715,2097151,4194303,8388607,3355443,33554431,
%U A213244 67108863,134217727
%N A213244 Number of nonzero elements in GF(2^n) that are 5th powers.
%H A213244 Vincenzo Librandi, <a href="/A213244/b213244.txt">Table of n, a(n) for n = 1..1000</a>
%H A213244 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 17, 0, 0, 0, -16).
%F A213244 a(n) = M / GCD( M, 5 ) where M=2^n-1.
%F A213244 Conjectures from _Colin Barker_, Aug 23 2014: (Start)
%F A213244 a(n) = 17*a(n-4)-16*a(n-8).
%F A213244 G.f.: x*(8*x^6+12*x^5+14*x^4+3*x^3+7*x^2+3*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(x^2+1)*(4*x^2+1)).
%F A213244 (End)
%p A213244 A213244:=n->(2^n-1)/gcd(2^n-1,5): seq(A213244(n), n=1..40); # _Wesley Ivan Hurt_, Aug 24 2014
%t A213244 Table[(2^n - 1)/GCD[2^n - 1, 5], {n, 50}] (* _Vincenzo Librandi_, Mar 16 2013 *)
%o A213244 (Magma) [(2^n - 1) / GCD (2^n - 1, 5): n in [1..40]]; // _Vincenzo Librandi_, Mar 16 2013
%o A213244 (PARI) a(n)=(2^n-1)/gcd(2^n-1,5) \\ _Edward Jiang_, Sep 04 2014
%Y A213244 Cf. A213243 (cubes), A213245 (7th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers).
%K A213244 nonn
%O A213244 1,2
%A A213244 _Joerg Arndt_, Jun 07 2012