12363Re: [PrimeNumbers] Number of factors in average
- May 5, 2003In a message dated 06/05/03 00:40:56 GMT Daylight Time, ambroxius@...
> I was thinking on prime factors rather than in divisors... the number ofthem is quite
> lesser than this of the divisors... what order has?Sorry, my fault.
That standard number theory function is Omega(n), defined to be the total
number of prime factors of n; in other words, if there is the prime
n = p_1^e_1 * ... * p_r^e_r,
Omega(n) = e_1 + ... + e_r.
So, in particular Omega(1) = 0. [As an aside: anyone who thinks 1 is a prime
would have a hard job defining Omega(); and 1 is certainly not composite...]
Omega(n) has average order log(log(n)).
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