Counts the number of Positive Integers less than or equal to a number which are not divisible by any of the first Primes,
(1) 

(2) 
Legendre's formula satisfies the Recurrence Relation
(3) 
(4) 
(5) 
(6) 
Note that is not practical for computing for large arguments. A more efficient modification is Meissel's Formula.
See also Lehmer's Formula, Mapes' Method, Meissel's Formula, Prime Counting Function