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A055671
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Number of prime Hurwitz quaternions of norm n.
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2
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0, 0, 24, 96, 0, 144, 0, 192, 0, 0, 0, 288, 0, 336, 0, 0, 0, 432, 0, 480, 0, 0, 0, 576, 0, 0, 0, 0, 0, 720, 0, 768, 0, 0, 0, 0, 0, 912, 0, 0, 0, 1008, 0, 1056, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 1440, 0, 1488, 0, 0, 0, 0, 0, 1632, 0, 0, 0, 1728, 0, 1776, 0, 0, 0, 0, 0
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OFFSET
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0,3
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REFERENCES
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L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.
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LINKS
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FORMULA
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a(n) = number of vectors of norm n in D_4 lattice (A004011) if n is a prime, otherwise a(n) = 0.
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MATHEMATICA
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a[p_?PrimeQ] := Reduce[ a^2 + b^2 + c^2 + d^2 == 4p, {a, b, c, d}, Integers] // Length; a[_] = 0; Table[ a[n], {n, 0, 78}] (* Jean-François Alcover, Oct 03 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jun 10 2005
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STATUS
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approved
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