A246655 Prime powers: numbers of the form p^k where p is a prime and k >= 1 

This is also the sequence of all possible sizes of a finite field.

It sounds identical to the sound of the primes.

Residue counts:
2   [19, 78715]
3   [12, 39432, 39290]
4   [18, 39373, 1, 39342]
5   [8, 19716, 19636, 19680, 19694]
6   [0, 39423, 10, 12, 9, 39280]
7   [7, 13138, 13132, 13107, 13136, 13108, 13106]
8   [17, 19741, 1, 19665, 1, 19632, 0, 19677]
9   [11, 13137, 13103, 1, 13133, 13073, 0, 13162, 13114]
10   [0, 19712, 5, 19675, 5, 8, 4, 19631, 5, 19689]
11   [5, 7899, 7847, 7859, 7880, 7894, 7881, 7879, 7877, 7869, 7844]
12   [0, 19748, 1, 6, 9, 19619, 0, 19675, 9, 6, 0, 19661]

Density information:
A(x) at x=10,100,1000,...:
[7, 35, 193, 1280, 9700, 78734]

A(x)/x at x=10,100,1000,...:
0.7,0.35,0.193,0.128,0.097,0.078734,

First 100 first differences:
[1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, 6, 
2, 3, 3, 4, 2, 6, 2, 2, 6, 8, 4, 2, 4, 2, 4, 8, 4, 2, 1, 3, 6, 2, 10, 
2, 6, 6, 4, 2, 4, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 2, 8, 5, 1, 
6, 6, 2, 6, 4, 2, 6, 4, 14, 4, 2, 4, 14, 6, 6, 4, 2, 4, 6, 2, 6, 6, 
6, 4, 6, 8, 4, 8, 10, 2]

First 99 second differences:
0,0,1,-1,0,1,0,1,-2,1,2,-2,0,0,0,-1,4,-1,-2,2,-2,2,2,-4,1,0,1,-2,4,
-4,0,4,2,-4,-2,2,-2,2,4,-4,-2,-1,2,3,-4,8,-8,4,0,-2,-2,2,2,-4,8,-8,2,
-2,10,0,-8,-2,2,2,-4,0,6,-3,-4,5,0,-4,4,-2,-2,4,-2,10,-10,-2,2,10,-8,
0,-2,-2,2,2,-4,4,0,0,-2,2,2,-4,4,2,-8,

The audio is indistinguishable from the sound of the primes, 
and similarly to the primes, there are some notable thick lines at 44100/6 = 7350hz and 44100/3 = 14700 hz
In residue classes of primes, for example 7, we can see that it is quite even excluding modulo 0. 
So in mod 7:[7, 13138, 13132, 13107, 13136, 13108, 13106] there are relatively
equal amounts of integers of form 7k+1,7k+2.....7k+6, numbers of form 7k must be a 
power of 7: 7,49... etc. The main difference from primes is that in the sequence of primes, 
the residue class of any prime p would start with 1 since any other number equal to 0 mod p 
would have to be divisible by p, which makes it composite. 

-Jayme Kim