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

1, 5, 73, 4369, 1082401, 1090785345, 4432676798593, 72340172838076673, 4731607904558235517441, 1239150146850664126585242625, 1298708349570020393652962442872833, 5445847423328601499764522166702896582657, 91355004067076339167413824240109498970069278721

Offset: 1

Author

Leroy Quet, Apr 19 2007

Keywords

• nonn

Comments

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

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A051156, A119408, A156585.

Programs

Maple

a:=n->(2^(n^2)-1)/(2^n-1): seq(a(n),n=1..13);

Mathematica

f[n_] := (2^(n^2) - 1)/(2^n - 1); Array[f, 12]
F[n_] := Plus @@ Table[2^((n - i)*n), {i, 1, n}] (* Enrique Pérez Herrero, Feb 23 2009 *)
Table[(2^(n^2) - 1)/(2^n - 1), {n, 1, 20}] (* Vincenzo Librandi, Feb 18 2014 *)

PARI

a(n)=(2^n^2-1)/(2^n-1) \\ Charles R Greathouse IV, Feb 17 2014

Formula

a(n) = Sum_{k=1..n} 2^((n-k)*n). - Enrique Pérez Herrero, Feb 23 2009

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Apr 22 2007