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A092205
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Number of units in the imaginary quadratic field Q(sqrt(-n)).
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5
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4, 2, 6, 4, 2, 2, 2, 2, 4, 2, 2, 6, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2
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OFFSET
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1,1
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Unit
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FORMULA
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EXAMPLE
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For n=1, the units are +/-1, +/-i, so a(1) = 4.
For n=3, the units are +/-1, +/-w, +/-w^2, where w is a cube root of unity, so a(3) = 6. [Corrected by Jonathan Sondow, Jan 29 2014]
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MAPLE
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A092205 := proc(n) if(type(sqrt(n), integer))then return 4: elif(n mod 3 = 0 and type(sqrt(n/3), integer))then return 6: else return 2: fi: end: seq(A092205(n), n=1..105); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
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a[n_] := Which[ IntegerQ[ Sqrt[n] ], 4, Mod[n, 3] == 0 && IntegerQ[ Sqrt[n/3] ], 6, True, 2]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Oct 30 2012, after Nathaniel Johnston *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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