How many $ mathbb {Q} $-base $$ It can be constructed from the set of vectors. $ log (1), cdots, log (n) $?

Data for $ n = 1,2,3 cdots $ computed with Sage:

$$ 1, 1, 1, 2, 2, 5, 5, 7, 11, 25, 25, 38, 38, 84, 150, 178, 178, 235, 235 $$

Context:

The real numbers $ log (p_1), cdots, log (p_r) $ where $ p_i $ Is it known that the i-th prime are linearly independent over the rational ones? $ mathbb {Q} $.

Example:

```
[{}] -> For n = 1, we have 1 = a (1) bases; We count {} as the basis for V_0 = {0}
[{2}] -> For n = 2, we have 1 = a base (2), which is {2};
[{2, 3}] -> for n = 3, we have 1 = a base (3), which is {2,3};
[{2, 3}, {3, 4}] -> for n = 4 we have 2 = a (4) bases, which are {2,3}, {3,4}
[{2, 3, 5}, {3, 4, 5}] -> a (5) = 2;
[{2, 3, 5}, {2, 5, 6}, {3, 4, 5}, {3, 5, 6}, {4, 5, 6}] -> a (6) = 5;
[{2, 3, 5, 7}, {2, 5, 6, 7}, {3, 4, 5, 7}, {3, 5, 6, 7}, {4, 5, 6, 7}] -> a (7) = 5.
```