- 1. number of prime powers

Posted by: "Werner D. Sand" Theo.3.1415@... theo2357

Date: Tue Dec 18, 2007 4:00 pm ((PST))

Who knows a good approximate formula for the number of prime powers up

to x (without simple prime numbers):

N = sum(1)(p^n <= x), p prime, n>1 ?

*******

Would this not be the number of primes < x

+ the number of primes < x^(1/2)

+ the number of primes < x^(1/3)

+ the number of primes < x^(1/4)

+ etc

approximately equal to

[ x + 2 * x^(1/2) + 3 * x^(1/3) + 4 * x^(1/4) + 5 * x^(1/5)

+ . . . ] / ln(x)

Kermit < kermit@... > - --- In primenumbers@yahoogroups.com, Kermit Rose <kermit@...> wrote:
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up

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> 1. number of prime powers

> Posted by: "Werner D. Sand" Theo.3.1415@... theo2357

> Date: Tue Dec 18, 2007 4:00 pm ((PST))

>

> Who knows a good approximate formula for the number of prime powers

> to x (without simple prime numbers):

(1/5)

> N = sum(1)(p^n <= x), p prime, n>1 ?

>

>

> *******

>

>

> Would this not be the number of primes < x

> + the number of primes < x^(1/2)

> + the number of primes < x^(1/3)

> + the number of primes < x^(1/4)

> + etc

>

>

> approximately equal to

>

> [ x + 2 * x^(1/2) + 3 * x^(1/3) + 4 * x^(1/4) + 5 * x^

> + . . . ] / ln(x)

That's allright. Can you sum it up into a closed form?

>

>

>

>

> Kermit < kermit@... >

WDS