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%I #4 Nov 09 2012 15:32:43
%S 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,
%T -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,
%U -2,0,2,3,6,5,16,0,0,-3,0,-3,0,0,3,0,3,0,1
%N Imaginary part of the arithmetic derivative for the triangle of Gaussian integers z = r + i*I, with r >= 0 and i >= 0.
%C The real part is in A218854. Consult A099379 for the arithmetic derivative of Gaussian integers.
%H T. D. Noe, <a href="/A218855/b218855.txt">Rows n = 0..100 of triangle, flattened</a>
%e Triangle:
%e 0
%e 0, 0
%e -2, 0, 2
%e 0, 0, 0, 1
%e -8, -2, 0, 2, 8
%e -3, 0, 0, 0, 0, 3
%e -6, -3, -2, 1, 2, 3, 8
%e 0, 0, 0, -2, 2, 0, 0, 1
%t 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}]]
%Y Cf. A099379, A099380.
%K sign,tabl
%O 0,4
%A _T. D. Noe_, Nov 09 2012
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