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 A055667 Number of Eisenstein-Jacobi primes of norm n. 7
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2. REFERENCES R. K. Guy, Unsolved Problems in Number Theory, A16. L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VI. LINKS Table of n, a(n) for n=0..99. FORMULA a(n) = 6 * A055668(n). - Franklin T. Adams-Watters, May 05 2006 EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A055664-A055668, A055025-A055029, A135461, A135462. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice. Sequence in context: A318537 A006806 A002892 * A281080 A283347 A334710 Adjacent sequences: A055664 A055665 A055666 * A055668 A055669 A055670 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Jun 09 2000 EXTENSIONS More terms from Franklin T. Adams-Watters, May 05 2006 STATUS approved

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Last modified December 8 15:23 EST 2023. Contains 367680 sequences. (Running on oeis4.)