is there a large list of highly composite number? I'm searching for some very big {more less $2^{1024}$} highly composite number (HCN), for a number theory experiment, so I asked myself "if there are prime list this size, why not HCN lists this size" so instead of searching them, I could just copy them, but I have not found any list enough big, I have just found this list: https://oeis.org/A002182/list but is verry small.
I could work with a not so big list, but I still need lots of very big, very composite numbers
 A: Here is a list of the first 10000 ones.
I found this in the External Links section of the highly composite number  Wikipedia page, which has at least one other link that you might find useful.
A: You can compute your (probably) own, if that is good enough.  If you look at the divisor function the number of divisors of a number $N$ that is $p^aq^br^c \ldots$ (with $p,q,r$ prime) is $(a+1)(b+1)(c+1)\ldots$.  Clearly you want $p=2, q=3, r=5$ and $a \ge b \ge c$ and so on.  Now if you increase $a$ by $1$, you multiply the number of factors by $\frac {a+2}{a+1}=1+\frac 1{a+1}$  If we consider $\Delta \frac {\log \sigma_0(N)}{\Delta \log N}$ for increasing the exponent on a prime $P$ that currently has exponent $A$, we get $ \frac {\Delta\log \sigma_0(N)}{\Delta \log N}\approx \frac{\frac 1{A+1}}{\log P}$  This expresses the ratio of the (log of) the additional factors we get to the increase in the (log of) $N$.  To have a highly composite number we want these ratios to be about the same.  They can't be absolutely the same because of the granularity of the primes and exponents.  You can pick a $k=\frac{\frac 1{A+1}}{\log P}$ and find $A=\frac 1{k \log P}-1$  If you pick $k=0.2$ and round all the numbers to the nearest integer, you get $2^6*3^4*5^2*7^2*11*13*17*19*23=6746328388800$, which is number $104$ on the list.  As you pick smaller positive $k$ you get bigger numbers.  Because of the granularity of integers, there will be other candidates.  If you really need the record setters, you should check around nearby exponents to find if the one you started with is really highly composite.
