A218855 Imaginary part of the arithmetic derivative for the triangle of Gaussian integers z = r + i*I, with r >= 0 and i >= 0.

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

Offset

0,4

Comments

The real part is in A218854. Consult A099379 for the arithmetic derivative of Gaussian integers.

Links

T. D. Noe, Rows n = 0..100 of triangle, flattened

Example

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

Mathematica

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}]]

Crossrefs

Cf. A099379, A099380.

Sequence in context: A231715 A137678 A359893 * A069517 A193526 A160498

Adjacent sequences: A218852 A218853 A218854 * A218856 A218857 A218858

Keyword

sign,tabl

Author

T. D. Noe, Nov 09 2012

Status

approved