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A112779 Largest exponent in the prime factorization of highly composite numbers (definition 1, A002182). 8


%S 0,1,2,1,2,3,2,4,2,3,2,4,3,4,3,2,4,3,4,3,5,4,6,4,3,4,5,4,3,5,4,6,4,5,

%T 4,5,6,4,3,5,4,6,4,5,4,5,6,4,6,7,5,4,4,6,4,5,4,5,6,4,6,7,5,4,4,6,5,5,

%U 4,6,5,6,4,6,7,5,4,6,5,7,6,5,6,4,4,6,7,5,5,4,6,6,5,7,6,5,6,4,7,6,7,5,7,6,8

%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.

%K nonn

%O 1,3

%A _Ray Chandler_, Nov 11 2005

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)