%I #12 Mar 01 2023 15:27:29
%S 0,0,0,6,6,0,0,12,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,6,0,0,0,0,0,12,
%T 0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,
%U 0,0,12,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0
%N Number of Eisenstein-Jacobi primes of norm n.
%C These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.
%D R. K. Guy, Unsolved Problems in Number Theory, A16.
%D L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VI.
%F a(n) = 6 * A055668(n). - _Franklin T. Adams-Watters_, May 05 2006
%e There are 6 Eisenstein-Jacobi primes of norm 3, omega-omega^2 times one of the 6 units [ +-1, +-omega, +-omega^2 ] but only one up to equivalence.
%t a[3] = 6; a[p_ /; PrimeQ[p] && Mod[p, 6] == 1] = 12; a[n_ /; PrimeQ[p = Sqrt[n]] && Mod[p, 3] == 2] = 6; a[_] = 0; Table[a[n], {n, 0, 99}] (* _Jean-François Alcover_, Oct 24 2013, after _Franklin T. Adams-Watters_ *)
%Y Cf. A055664-A055668, A055025-A055029, A135461, A135462. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice.
%K nonn,easy,nice
%O 0,4
%A _N. J. A. Sloane_, Jun 09 2000
%E More terms from _Franklin T. Adams-Watters_, May 05 2006