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

as in 12, 36,225 ). Perhaps a general formula for n prime factors? - 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: 4,6,9,10,14,15,21,22…? (NOT: 2 different prime factors

as in 12, 36,225…). Perhaps a general formula for n prime factors? - 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?

> - 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:>

factors?

> 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

> >

>