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A128889 a(n) = (2^(n^2) - 1)/(2^n - 1).

%I A128889 #40 Apr 20 2020 14:47:11
%S A128889 1,5,73,4369,1082401,1090785345,4432676798593,72340172838076673,
%T A128889 4731607904558235517441,1239150146850664126585242625,
%U A128889 1298708349570020393652962442872833,5445847423328601499764522166702896582657,91355004067076339167413824240109498970069278721
%N A128889 a(n) = (2^(n^2) - 1)/(2^n - 1).
%C A128889 a(n) is prime for n in A156585. Conjecture: gpf(a(n)) = gpf(Phi(n,2^n)), where Phi(n,2^n) = A070526(n). - _Thomas Ordowski_, Feb 16 2014
%C A128889 The conjecture fails at n = 26, where 3340762283952395329506327023033 > 215656329382891550920192462661. Next counterexample for n = 30, but no odd counterexamples found so far. - _Charles R Greathouse IV_, Feb 17 2014
%H A128889 Vincenzo Librandi, <a href="/A128889/b128889.txt">Table of n, a(n) for n = 1..50</a>
%F A128889 a(n) = Sum_{k=1..n} 2^((n-k)*n). - _Enrique Pérez Herrero_, Feb 23 2009
%p A128889 a:=n->(2^(n^2)-1)/(2^n-1): seq(a(n),n=1..13);
%t A128889 f[n_] := (2^(n^2) - 1)/(2^n - 1); Array[f, 12]
%t A128889 F[n_] := Plus @@ Table[2^((n - i)*n), {i, 1, n}] (* _Enrique Pérez Herrero_, Feb 23 2009 *)
%t A128889 Table[(2^(n^2) - 1)/(2^n - 1), {n, 1, 20}] (* _Vincenzo Librandi_, Feb 18 2014 *)
%o A128889 (PARI) a(n)=(2^n^2-1)/(2^n-1) \\ _Charles R Greathouse IV_, Feb 17 2014
%Y A128889 Cf. A051156, A119408, A156585.
%K A128889 nonn
%O A128889 1,2
%A A128889 _Leroy Quet_, Apr 19 2007
%E A128889 More terms from _Robert G. Wilson v_ and _Emeric Deutsch_, Apr 22 2007