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A218855
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Imaginary part of the arithmetic derivative for the triangle of Gaussian integers z = r + i*I, with r >= 0 and i >= 0.
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4
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0, 0, 0, -2, 0, 2, 0, 0, 0, 1, -8, -2, 0, 2, 8, -3, 0, 0, 0, 0, 3, -6, -3, -2, 1, 2, 3, 8, 0, 0, 0, -2, 2, 0, 0, 1, -24, -5, -8, -2, 0, 2, 8, 5, 24, 0, -4, 0, 1, 0, 0, 2, 0, 4, 6, -16, -5, -6, -3, -2, 0, 2, 3, 6, 5, 16, 0, 0, -3, 0, -3, 0, 0, 3, 0, 3, 0, 1
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OFFSET
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0,4
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COMMENTS
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The real part is in A218854. Consult A099379 for the arithmetic derivative of Gaussian integers.
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LINKS
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EXAMPLE
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Triangle:
0
0, 0
-2, 0, 2
0, 0, 0, 1
-8, -2, 0, 2, 8
-3, 0, 0, 0, 0, 3
-6, -3, -2, 1, 2, 3, 8
0, 0, 0, -2, 2, 0, 0, 1
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MATHEMATICA
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di[0]=0; di[1]=0; di[ -1]=0; di[I]=0; di[ -I]=0; di[n_] := Module[{f, unt}, f=FactorInteger[n, GaussianIntegers->True]; unt=(Abs[f[[1, 1]]]==1); If[unt, f=Delete[f, 1]]; f=Transpose[f]; Plus@@(n*f[[2]]/f[[1]])]; Im[Table[di[n-i + I*i], {n, 0, 12}, {i, 0, n}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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