PL-OM 2021 Problem 1

Let $p_i$ for $i=1,2,..., k$ be a sequence of smallest consecutive prime numbers ( $p_1=2$ , $p_2=3$ , $p_3=3$ etc. ). Let $N=p_1\cdot p_2 \cdot ... \cdot p_k$ . Prove that in a set $\{ 1,2,...,N \}$ there exist exactly $\frac{N}{2}$ numbers which are divisible by odd number of primes $p_i$ .