A Formula that Sends Primes Into Integers And Composites Into Fractions

Here we introduce a formula that sends primes numbers into natural numbers and composite into fractions.
L(n)=π(n) +(n-p_π(n))/Δ
where π(n) is the prime-counting function and Δ is the gap between two consecutive primes.
We calculate the first few numbers.
L(1) = 0, L(2) = 1, L(3) = 2, L(4) = 2.5, L(5) = 3, L(6) = 3.5, L(7) = 4, L(8) = 4.25, L(9) = 4.5, L(10) = 4.75, and L(11) = 5.
It can be noticed that it sends primes into natural numbers and composites into fractions.