## Divisibility streaks

### Problem 601

For every positive number $n$ we define the function $streak(n)=k$ as the smallest positive integer $k$ such that $n+k$ is not divisible by $k+1$.

E.g:

13 is divisible by 1

14 is divisible by 2

15 is divisible by 3

16 is divisible by 4

17 is NOT divisible by 5

So $streak(13) = 4$.

Similarly:

120 is divisible by 1

121 is NOT divisible by 2

So $streak(120) = 1$.

Define $P(s, N)$ to be the number of integers $n$, $1 < n < N$, for which $streak(n) = s$.

So $P(3, 14) = 1$ and $P(6, 10^6) = 14286$.

Find the sum, as $i$ ranges from 1 to 31, of $P(i, 4^i)$.