In a message dated 06/05/03 00:40:56 GMT Daylight Time,

ambroxius@...
writes:

> I was thinking on prime factors rather than in divisors... the number of

them 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

factorisation

n = p_1^e_1 * ... * p_r^e_r,

then

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)).

Mike

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