Integer Sequences

Triangle of the number of prime factors (counted multiply) of first-quadrant Guassian integers.

0, 0, 0, 2, 1, 2, 1, 1, 1, 1, 4, 2, 3, 2, 4, 2, 1, 1, 1, 1, 2, 3, 2, 3, 2, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 6, 3, 4, 2, 5, 2, 4, 3, 6, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 4, 2, 3, 2, 3, 3, 3, 2, 3, 2, 4, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 5, 2, 4, 3, 5, 2, 4, 2, 5

0

Note that the table is symmetric.

T. D. Noe, Plot of 101 rows

T. D. Noe, Table of 101 rows

Eric W. Weinstein, MathWorld: Gaussian Integers

Triangle:
0
0, 0
2, 1, 2
1, 1, 1, 1
4, 2, 3, 2, 4
2, 1, 1, 1, 1, 2
3, 2, 3, 2, 3, 2, 3
1, 1, 1, 2, 2, 1, 1, 1
6, 3, 4, 2, 5, 2, 4, 3, 6
2, 2, 1, 2, 1, 1, 2, 1, 2, 2

(Mma) Table[z = i - j + I*j; f = FactorInteger[z, GaussianIntegers -> True]; If[Abs[z] <= 1, 0, If[Abs[f[[1, 1]]] <= 1, f = Rest[f]]; Total[Transpose[f][[2]]]], {i, 0, 10}, {j, 0, i}]

Cf. S000404, S000406.

nonn,tabl

T. D. Noe, Dec 10 2014