Integer Sequences

Triangle of the number of divisors of first-quadrant Guassian integers.

0, 1, 1, 3, 2, 3, 2, 2, 2, 2, 5, 4, 4, 4, 5, 4, 2, 2, 2, 2, 4, 6, 4, 6, 4, 6, 4, 6, 2, 2, 2, 3, 3, 2, 2, 2, 7, 6, 8, 4, 6, 4, 8, 6, 7, 3, 4, 2, 4, 2, 2, 4, 2, 4, 3, 12, 4, 6, 4, 6, 8, 6, 4, 6, 4, 12, 2, 2, 4, 2, 4, 2, 2, 4, 2, 4, 2, 2, 10, 4, 8, 8, 10, 4, 8, 4

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
1, 1
3, 2, 3
2, 2, 2, 2
5, 4, 4, 4, 5
4, 2, 2, 2, 2, 4
6, 4, 6, 4, 6, 4, 6
2, 2, 2, 3, 3, 2, 2, 2
7, 6, 8, 4, 6, 4, 8, 6, 7
3, 4, 2, 4, 2, 2, 4, 2, 4, 3

(Mma) Table[z = i - j + I*j; If[z == 0, 0, f = Length[Divisors[z, GaussianIntegers -> True]]], {i, 0, 10}, {j, 0, i}]

Cf. S000404, S000405.

nonn,tabl

T. D. Noe, Dec 10 2014