# Prime divisors of factorials

1. Oct 17, 2004

### Ethereal

I was reading this tutorial and I came across this part which I didn't quite understand:

I don't follow this. What does "a will be counted j times and will contribute i towards t" mean? Why does this show that t=s?

2. Oct 17, 2004

### TenaliRaman

First get this clear ...
m1 denotes the number of values in {1,..,n} divisible by p
m2 denotes the number of values in {1,..,n} divisible by p^2
m3 denotes the number of values in {1,..,n} divisible by p^3
...
...
mk denotes the number of values in {1,..,n} divisible by p^k

if a is divisible by p^j and not by p^j+1
that means the maximum power of p that can divide a is j ...

if p^j|a then p|a,p^2|a,p^3|a,p^4|a,.....,p^j|a

that means this number a will have been counted in m1,m2,m3,m4,....,mj
t = sum of all m_i's
so a will have been counted j times in t ....

or in other words contribute an m_i towards t
(can u see why?)

set a=n and apply floor

-- AI