50400: A Highly Composite Number

This blog recently had its 50400th visitor. The number 50400 is the 27th highly composite number. A highly composite number has more divisors than all previous highly composite numbers. In the case of 50400, it has 108 divisors.

The first 27 highly composite numbers and the number of their divisors are:

Order	Highly Composite Number	Number of Divisors
1	1	1
2	2	2
3	4	3
4	6	4
5	12	6
6	24	8
7	36	9
8	48	10
9	60	12
10	120	16
11	180	18
12	240	20
13	360	24
14	720	30
15	840	32
16	1260	36
17	1680	40
18	2520	48
19	5040	60
20	7560	64
21	10080	72
22	15120	80
23	20160	84
24	25200	90
25	27720	96
26	45360	100
27	50400	108

The highly composite numbers are designated in the On-Line Encyclopedia of Integer Sequences as A002182 , and the number of their divisors is the sequence A002183.