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From: master1729 on 30 May 2010 12:31
Let T(x) denote the number of squarefree integers between 1 and x.

T(x) = 6 * pi^-2 * x + O( x^(1-ln(2)) )

this is my teenage challange , tommy's jugendtraum if you like.


regards

tommy1729
From: Spotter on 30 May 2010 16:41
"NNTP-Posting-Host: gallium.mathforum.org"

Mathforum fuckwit.

"master1729" <tommy1729(a)gmail.com> wrote in message
news:2126894270.251348.1275251507459.JavaMail.root(a)gallium.mathforum.org...
> Let T(brane) no brane a tall <


From: christian.bau on 30 May 2010 17:50
On May 30, 9:31 pm, master1729 <tommy1...(a)gmail.com> wrote:
> Let T(x) denote the number of squarefree integers between 1 and x.
>
> T(x) = 6 * pi^-2 * x + O( x^(1-ln(2)) )

Well, so what about it?

> this is my teenage challange , tommy's jugendtraum if you like.

I can see "jugendtraum" is German (except that it should start with a
capital letter). I don't quite get "challange". Is that some french
word? Can't find it in any dictionary.
From: Roy Simms on 30 May 2010 21:11
On May 30, 1:31 pm, master1729 <tommy1...(a)gmail.com> wrote:
> Let T(x) denote the number of squarefree integers between 1 and x.
>
> T(x) = 6 * pi^-2 * x + O( x^(1-ln(2)) )
>
> this is my teenage challange , tommy's jugendtraum if you like.
>
> regards
>
> tommy1729

Posting teh someting making teh sense, you brainless spamming troll.

From: Rob Johnson on 31 May 2010 18:07
In article <2126894270.251348.1275251507459.JavaMail.root(a)gallium.mathforum.org>,
master1729 <tommy1729(a)gmail.com> wrote:
>Let T(x) denote the number of squarefree integers between 1 and x.
>
>T(x) = 6 * pi^-2 * x + O( x^(1-ln(2)) )
>
>this is my teenage challange , tommy's jugendtraum if you like.

The fact that T(x)/x ~ 6/pi^2 is easy, so your question is about the
remainder: O(x^{-ln(2)}).

Considering empirical data for small n, it looks as if the remainder
very small:

n
--- 2 6n
n > mu (k) ---- |diff|
--- pi^2
k=1

100 61 61 0
1000 608 608 0
10000 6083 6079 4
100000 60794 60793 1
1000000 607926 607927 1
10000000 6079291 6079271 20
100000000 60792694 60792710 16

However, <http://en.wikipedia.org/wiki/Square-free_integer>
says that The Riemann Hypothesis implies that the remainder is
O(x^{-37/54+e}) for any e > 0. Unfortunately, -ln(2) < -37/54,
so getting the remainder estimate you want may be difficult.

Rob Johnson <rob(a)trash.whim.org>
take out the trash before replying
to view any ASCII art, display article in a monospaced font
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