I wouldn't call sum(something) a formula, but a calculating

instruction. For example pi(x) = sum(1)(2,3,5
x) looks great, but is

only an instruction to count primes up to x, while the formula is

pi(x) ~ x/ln x. Thus pi(2)(x) = sum (pi(x/p i)-i+1) (i=1
pi(x^(1/2))

looks very spectacular, but is only the description of counting the

semiprimes up to x. The formula for it might be

pi(2)(x) ~ n/(e ln ln x) or the like, perhaps someone knows a better

one.

Werner

--- In

primenumbers@yahoogroups.com, "Werner D. Sand"

<Theo.3.1415@...> wrote:

>

> Perfect answer! Thank you, Mike.

>

>

>

>

> --- In primenumbers@yahoogroups.com, mikeoakes2@ wrote:

> >

> > An integer with exactly k prime factors is somethimes called a

> > k-almost-prime.

> >

> > Here's a link:-

> > http://mathworld.wolfram.com/AlmostPrime.html

> >

> > -Mike Oakes

> >

> >

> > -----Original Message-----

> > From: Theo.3.1415@

> > To: primenumbers@yahoogroups.com

> > Sent: Wed, 31 Jan 2007 9.13AM

> > Subject: [PrimeNumbers] Two prime factors formula?

> >

> > Does anyone know an approximate formula (according to x/ln x) for

> the

> > number of positive integers up to x which are the product of

> exactly 2

> > prime factors: 4,6,9,10,14,15,21,22â¦? (NOT: 2 different prime

> factors

> > as in 12, 36,225â¦). Perhaps a general formula for n prime

factors?

> >

>