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A213246 Number of nonzero elements in GF(2^n) that are 9th powers. 8
1, 1, 7, 5, 31, 7, 127, 85, 511, 341, 2047, 455, 8191, 5461, 32767, 21845, 131071, 29127, 524287, 349525, 2097151, 1398101, 8388607, 1864135, 33554431, 22369621, 134217727, 89478485, 536870911, 119304647, 2147483647, 1431655765, 8589934591, 5726623061, 34359738367, 7635497415 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,65,0,0,0,0,0,-64).

FORMULA

a(n) = M / gcd( M, 9 ), where M=2^n-1.

Conjectures from Colin Barker, Aug 23 2014: (Start)

a(n) = 65*a(n-6)-64*a(n-12).

G.f.: x*(2*x^2 -x +1)*(16*x^8 +16*x^7 +28*x^6 +16*x^5 +25*x^4 +8*x^3 +7*x^2 +2*x +1) / ((x -1)*(x +1)*(2*x -1)*(2*x +1)*(x^2 -x +1)*(x^2 +x +1)*(4*x^2 -2*x +1)*(4*x^2 +2*x +1)). (End)

Conjectures verified by Robert Israel, Jun 27 2018.

MAPLE

A213246:=n->(2^n-1)/gcd(2^n-1, 9): seq(A213246(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

MATHEMATICA

Table[(2^n - 1)/GCD[2^n - 1, 9], {n, 100}] (* Vincenzo Librandi, Mar 15 2013 *)

PROG

(MAGMA) [(2^n-1)/GCD(2^n-1, 9): n in [1..40]]; // Vincenzo Librandi, Mar 15 2013

(PARI) a(n)=(2^n-1)/gcd(2^n-1, 9) \\ Edward Jiang, Sep 04 2014

(GAP) List([1..40], n->(2^n-1)/Gcd(2^n-1, 9)); # Muniru A Asiru, Jun 27 2018

CROSSREFS

Cf. A213243 (cubes), A213244 (5th powers), A213245 (7th powers), A213247 (11th powers), A213248 (13th powers).

Sequence in context: A120404 A146619 A059990 * A213243 A185269 A070426

Adjacent sequences:  A213243 A213244 A213245 * A213247 A213248 A213249

KEYWORD

nonn,easy

AUTHOR

Joerg Arndt, Jun 07 2012

STATUS

approved

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Last modified August 15 20:49 EDT 2018. Contains 313779 sequences. (Running on oeis4.)