Three-dimensional triangle of the conductor of a, b and c for the expression a*x + b*y + c*z.

2, 2, 4, 3, 2, 0, 6, 4, 8, 8, 2, 6, 6, 4, 5, 7, 6, 12, 10, 10, 2, 0, 6, 4, 8, 12, 0, 14, 0, 10, 6, 6, 18, 12, 18, 2, 8, 6, 4, 8, 12, 8, 0, 12, 14, 6, 12, 11, 14, 18, 8, 14, 24, 13, 20, 21, 2, 0, 6, 4, 8, 12, 0, 18, 0, 20, 6, 12, 14, 24, 16, 0, 8, 0, 28, 0, 20, 8, 18, 16, 32, 24, 23, 32

4

We assume 1 < a < b < c. The numbers x, y, and z are assumed to be nonnegative. The conductor is infinite (which is written as 0 here) when the GCD of (a,b,c) is greater than 1.

T. D. Noe, Plot of rows 4 to 40

T. D. Noe, Table of rows 4 to 40

David Bessoud and Stan Wagon, A Course in Computational Number Theory, Key College Publishing, 2000.

(Mma) Needs["CNT`”]; nn = 10; Table[d = Conductor[{a, b, c}]; If[d == Infinity, d = 0]; d, {c, 4, nn}, {b, 3, c - 1}, {a, 2, b - 1}]

Cf. S000429, S000430, S000432, S000433.

nonn,tabf

T. D. Noe, Dec 24 2014