%N Largest exponent in the prime factorization of highly composite numbers (definition 1, A002182).
%C Each highly composite number can be written as the product of primorials (A002110). This is also the number of primorials used in the product.
%C 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
%H T. D. Noe, <a href="/A112779/b112779.txt">Table of n, a(n) for n=1..10000</a> (using Flammenkamp's data)
%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">First 1200 highly composite numbers</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly Composite Number</a>
%e A002182(8) = 48 = 2^4*3, which has largest exponent 4, so a(8)=4.
%Y Cf. A002110, A002182, A002183, A007814, A108602, A112778, A112780, A112781.
%A _Ray Chandler_, Nov 11 2005