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A253655 Number of monic irreducible polynomials of degree 6 over GF(prime(n)). 1
9, 116, 2580, 19544, 295020, 804076, 4022064, 7839780, 24670536, 99133020, 147912160, 427612404, 791672280, 1053546956, 1796518224, 3694034916, 7030054140, 8586690620, 15076346164, 21349986840, 25222305336, 40514492720, 54489965796, 82830096360, 138828513824, 176919851700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (p^6 - p^3 - p^2 + p)/6, where p = prime(n).

EXAMPLE

For n=1 the a(1) = 9 irreducible monic polynomials of degree 6 over GF(2) are

x^6+x^5+1, x^6+x^3+1, x^6+x^5+x^4+x^2+1, x^6+x^5+x^3+x^2+1, x^6+x+1, x^6+x^5+x^4+x+1, x^6+x^4+x^3+x+1, x^6+x^5+x^2+x+1, x^6+x^4+x^2+x+1.

MAPLE

f:= p-> (p^6 - p^3 - p^2 + p)/6:

seq(f(ithprime(i)), i=1..100); # Robert Israel, Jan 07 2015

MATHEMATICA

Table[(Prime[n]^6 - Prime[n]^3 - Prime[n]^2 + Prime[n]) / 6, {n, 1, 30}] (* Vincenzo Librandi, Jan 08 2015 *)

PROG

(MAGMA) [(p^6 - p^3 - p^2 + p) div 6: p in PrimesUpTo(110)]; // Vincenzo Librandi, Jan 08 2015

CROSSREFS

Cf. A008837, A127919, A138420, A138426.

Sequence in context: A180913 A083305 A222146 * A092913 A022607 A139740

Adjacent sequences:  A253652 A253653 A253654 * A253656 A253657 A253658

KEYWORD

nonn

AUTHOR

Robert Israel, Jan 07 2015

STATUS

approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)