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A055668
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Number of inequivalent Eisenstein-Jacobi primes of norm n.
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5
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0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.
Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-omega, +-omega^2).
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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.
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FORMULA
| a(n) = 2 if n is a prime = 1 (mod 6); a(n) = 1 if n = 3 or n = p^2 where p is a prime = 2 (mod 3); a(n) = 0 otherwise. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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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.
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CROSSREFS
| Cf. A055664-A055667, A055025-A055029. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice.
Sequence in context: A089798 A070536 A030201 * A045839 A000086 A045838
Adjacent sequences: A055665 A055666 A055667 * A055669 A055670 A055671
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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