A218854 Real 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, 1, 2, 1, 1, 1, 0, 8, 3, 6, 3, 8, 3, 1, 1, 1, 1, 3, 8, 4, 8, 4, 8, 4, 6, 1, 1, 1, 4, 4, 1, 1, 0, 24, 10, 14, 5, 20, 5, 14, 10, 24, 6, 4, 1, 5, 1, 1, 4, 1, 4, 0, 16, 6, 12, 6, 12, 11, 12, 6, 12, 6, 16, 1, 1, 5, 1, 5, 1, 1, 5, 1, 5, 1, 0, 28, 7, 20

Offset

0,4

Comments

See A218856 for a two-dimensional plot of the derivatives. The imaginary part is in A218855. 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, 1, 2,
1, 1, 1, 0,
8, 3, 6, 3, 8,
3, 1, 1, 1, 1, 3,
8, 4, 8, 4, 8, 4, 6,
1, 1, 1, 4, 4, 1, 1, 0

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]])]; Re[Table[di[n-i + I*i], {n, 0, 12}, {i, 0, n}]]

Crossrefs

Cf. A099379, A099380.

Sequence in context: A287368 A108149 A128583 * A172303 A064391 A236470

Adjacent sequences: A218851 A218852 A218853 * A218855 A218856 A218857

Keyword

nonn,tabl

Author

T. D. Noe, Nov 09 2012

Status

approved