Each highly composite number can be written as the product of primorials (A002110). This is also the number of primorials used in the product.

a(i) = m where m is the exponent of 2 in the prime factorization of A002182(i), i.e., a(n) is the 2-adic valuation of A002182(n). For 2-adic valuation, see A007814, which gives a(n) = A007814(A002182(n)). - David A. Corneth, Aug 16 2015