Re: Factoraization of n! as power of primes


Gerard Schildberger wrote:
| Arturo Magidin wrote:
|> Abdulla wrote:
|> Hi everyone,
|> I wanna ask if anyone know where i can get a formula to the
|> factoraization of n! as a product of powers of primes i.e. n!=p1^e1 *
|> p2^e2 *.... where e1,e2,e3 are nonnegative integers and the formula
|> will provide them.
| There is no simple factorization.

|> can anyone tell me in which book i can get a formula like this ???
| Your dreams?

I've written an algorithm to do just that, it's not complicated at all
and quite simple to understand.

I misread the original and cancelled my posting.

I thought the original poster wanted to obtain BOTH the list of primes
and their exponents. Of course, it is easy, given a prime p and a
positive integer n, to find the exponent of p in the factorization of
n!. But there is no easy way to find all the primes that occur in the
factorization of n! given only n; at least, no known way. Otherwise,
figuring out if n is a prime would be easy, not to mention factoring:
just factor n! and factor (n-1)! to find a factorization for n.

Arturo Magidin, sans .sig

.

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