A253655 Number of monic irreducible polynomials of degree 6 over GF(prime(n)).

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

Offset: 1

Author

Robert Israel, Jan 07 2015

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A008837, A127919, A138420, A138426.

Programs

Magma

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

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 *)

Formula

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