prime factorizations of some small highly composite numbers

All highly composite numbers have prime factorizations containing consecutive prime numbers, starting with 2, while the exponents form a sequence in descending order (the number 1 as an exponent is tacit in the following table).

HCN	Factorization
4	$2^2$
6	$2\times 3$
12	$2^2\times 3$
24	$2^3\times 3$
36	$2^2\times 3^2$
48	$2^4\times 3$
60	$2^2\times 3\times 5$
120	$2^3\times 3\times 5$
180	$2^2\times 3^2\times 5$
240	$2^4\times 3\times 5$
360	$2^3\times 3^2\times 5$
720	$2^4\times 3^2\times 5$
840	$2^3\times 3\times 5\times 7$
1260	$2^2\times 3^2\times 5\times 7$
1680	$2^4\times 3\times 5\times 7$
2520	$2^3\times 3^2\times 5\times 7$
5040	$2^4\times 3^2\times 5\times 7$
7560	$2^3\times 3^3\times 5\times 7$
10080	$2^5\times 3^2\times 5\times 7$
15120	$2^4\times 3^3\times 5\times 7$
20160	$2^6\times 3^2\times 5\times 7$
25200	$2^4\times 3^2\times 5^2\times 7$
27720	$2^3\times 3^2\times 5\times 7\times 11$
45360	$2^4\times 3^4\times 5\times 7$
50400	$2^5\times 3^2\times 5^2\times 7$
55440	$2^4\times 3^2\times 5\times 7\times 11$
83160	$2^3\times 3^3\times 5\times 7\times 11$
110880	$2^5\times 3^2\times 5\times 7\times 11$
166320	$2^4\times 3^3\times 5\times 7\times 11$
221760	$2^6\times 3^2\times 5\times 7\times 11$
277200	$2^4\times 3^2\times 5^2\times 7\times 11$
332640	$2^5\times 3^3\times 5\times 7\times 11$
498960	$2^4\times 3^4\times 5\times 7\times 11$
554400	$2^5\times 3^2\times 5^2\times 7\times 11$
665280	$2^6\times 3^3\times 5\times 7\times 11$
720720	$2^4\times 3^2\times 5\times 7\times 11\times 13$
1081080	$2^3\times 3^3\times 5\times 7\times 11\times 13$
1441440	$2^5\times 3^2\times 5\times 7\times 11\times 13$
2162160	$2^4\times 3^3\times 5\times 7\times 11\times 13$

Title	prime factorizations of some small highly composite numbers
Canonical name	PrimeFactorizationsOfSomeSmallHighlyCompositeNumbers
Date of creation	2013-03-22 18:51:29
Last modified on	2013-03-22 18:51:29
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Example
Classification	msc 11N56