## Two prime factors formula?

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• 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:
Message 1 of 4 , Jan 31, 2007
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 ...
Message 2 of 4 , Jan 31, 2007
An integer with exactly k prime factors is somethimes called a
k-almost-prime.

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

-Mike Oakes

-----Original Message-----
From: Theo.3.1415@...
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. ... the ... exactly 2 ... factors
Message 3 of 4 , Jan 31, 2007

>
> An integer with exactly k prime factors is somethimes called a
> k-almost-prime.
>
> http://mathworld.wolfram.com/AlmostPrime.html
>
> -Mike Oakes
>
>
> -----Original Message-----
> From: Theo.3.1415@...
> 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
Message 4 of 4 , Feb 2, 2007
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.
> >
> > http://mathworld.wolfram.com/AlmostPrime.html
> >
> > -Mike Oakes
> >
> >
> > -----Original Message-----
> > From: Theo.3.1415@
> > 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?
> >
>
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