How many numbers 1 - n are divisible by a range of primes

Question

Hello, there was interesting simple math problem I have recently solved :

- How many positive integers in a range 1 to n are divisible by at least one of given primes ?

 

Here is the recursive function that solves the problem :

 

// n range of numbers from 1 to n
// p array of primes for divisibility check
long f(long n, long [] p)
{
    if(p.Length==0)
        return 0;

    long [] q = new long[p.Length-1];

    Array.Copy(p,1,q,0,p.Length-1);

    long r = (n/p[0])- (f(n/p[0],q)) + (f(n,q));

    return r;
}

 My question is :

- Is it possible to write this function in C# differently so that its execution becomes faster ?

 

All the best,

Željko Peric