The first Gaussian integer having n distinct prime factors in the triangle S000404.
0, 0, 2, 0, 3, 1, 10, 0, 30, 0, 75, 15, 315, 15, 1275, 255, 6630, 0, 29835, 3315
0
If there is more than one, we choose the one closest to the real axis.
T. D. Noe, Plot of 10 pairs
Eric W. Weinstein, MathWorld: Gaussian Integers
(Mma) n = 1; i = 0; While[n <= 7, i++; p2 = Table[z = i - j + I*j; f = FactorInteger[z, GaussianIntegers -> True]; If[Abs[f[[1, 1]]] <= 1, f = Rest[f]]; Length[f], {j, 0, Ceiling[i/2]}]; mx = Max[p2]; If[mx >= n, pos = Position[p2, mx, 1, 1][[1, 1]] - 1; Print[{mx, i - pos, pos, FactorInteger[i - pos + pos*I, GaussianIntegers -> True]}]; n++]]
nonn,more
T. D. Noe, Dec 12 2014