|
%I #11 Sep 08 2022 08:46:10
%S 9,116,2580,19544,295020,804076,4022064,7839780,24670536,99133020,
%T 147912160,427612404,791672280,1053546956,1796518224,3694034916,
%U 7030054140,8586690620,15076346164,21349986840,25222305336,40514492720,54489965796,82830096360,138828513824,176919851700
%N Number of monic irreducible polynomials of degree 6 over GF(prime(n)).
%H Robert Israel, <a href="/A253655/b253655.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (p^6 - p^3 - p^2 + p)/6, where p = prime(n).
%e For n=1 the a(1) = 9 irreducible monic polynomials of degree 6 over GF(2) are
%e 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.
%p f:= p-> (p^6 - p^3 - p^2 + p)/6:
%p seq(f(ithprime(i)), i=1..100); # _Robert Israel_, Jan 07 2015
%t Table[(Prime[n]^6 - Prime[n]^3 - Prime[n]^2 + Prime[n]) / 6, {n, 1, 30}] (* _Vincenzo Librandi_, Jan 08 2015 *)
%o (Magma) [(p^6 - p^3 - p^2 + p) div 6: p in PrimesUpTo(110)]; // _Vincenzo Librandi_, Jan 08 2015
%Y Cf. A008837, A127919, A138420, A138426.
%K nonn
%O 1,1
%A _Robert Israel_, Jan 07 2015
|
