The total number of factors in the decomposition of A007357(n) in terms of A050376 is A187043(n). The subset of factors which are ordinary primes are counted here.

The unique expansion of A007357(2)= 60 as a product of terms of A050376 is 3*4*5. Two of these factors, namely 3 and 5, are primes (A000040), so a(2)=2.