There is a more interesting form:
E^((4 I Pi (1 + 2^x x)) / (-3 + (-1)^x - 2 x))
which doesn't require floor's and gives you1s for primes:
{1, 1, 1, E^((2*I*Pi)/3), 1, 1, E^((2*I*Pi)/5), 1, 1, E^((2*I*Pi)/7), 1, E^(-((4*I*Pi)/5)), E^((8*I*Pi)/9), 1, 1, E^((2*I*Pi)/11), E^((16*I*Pi)/35), 1, E^((2*I*Pi)/13), 1, 1, E^(-((2*I*Pi)/3)), 1, E^((4*I*Pi)/7), E^((2*I*Pi)/17), 1, E^(-((14*I*Pi)/55)), E^((2*I*Pi)/19), 1, 1, E^((2*I*Pi)/21), E^((6*I*Pi)/13), 1, E^((2*I*Pi)/23), 1, 1, E^((22*I*Pi)/25), E^((16*I*Pi)/77), 1, E^((26*I*Pi)/27), 1, E^((6*I*Pi)/17), E^((2*I*Pi)/29), 1, E^(-((8*I*Pi)/13)), E^((2*I*Pi)/31), E^(-((84*I*Pi)/95)), 1, E^(-((28*I*Pi)/33)), 1}
This was found by replacing floor with the equivalent Fourier derived square-wave, aligned on the integer line.