There are over 16 million ways to give each of the integers

There are over 16 million ways to give each of the integers 1 through 24 one of two colors. A proper coloring occurs when all 24 numbers are colored so that for every integer d, every even length sequence of the form d, 2d, 3d, . . . has an equal number of each color. Find such a coloring or show that no such coloring exists.

The colouring is will be:

= d, d+2d, d+2d+3d, d+2d=3d+4d, ...