       Re: Hurwitz Zeta Rational Sequence showing primes in the denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg110102] Re: Hurwitz Zeta Rational Sequence showing primes in the denominator
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Tue, 1 Jun 2010 07:46:56 -0400 (EDT)
• References: <hu2g07\$kus\$1@smc.vnet.net>

```GHMM wrote:

> I've been looking at a zeta function to produce the primes and have
> come up with the following:
>
> Table[D[FindSequenceFunction[Table[Rationalize[ i^m N[Zeta[1 - m, (-i
> - 1)/i] + Zeta[1 - m, -(1/i)], 80]], {i, 80}] , n],{n, m}], {m, 30}]
>
> output :
>
> 2, 5/3, 6, 122/5, 120, 5000/7, 5040, 40656, 362880, 39312000/11,
> 39916800, 6489711360/13, 6227020800, 72648576000, 1307674368000,
> 671011307366400/17, 355687428096000, -(621352061890560000/19),
> 121645100408832000, 131163645205064908800, 51090942171709440000, -
> (14526772739252431257600000/23)...
>
> sequence into a product, the denominators are the primes.
>
> Ray
>

Suppose your table is tt. Then define:

schoen[{x_,y_}]:=HoldForm[x^y]
zerlege[expr_Integer] := Times @@ schoen /@ FactorInteger[expr]
zerlege[expr_Rational] := zerlege[Numerator[expr]]/Denominator[expr]

and do

zerlege/@tt

It seams, that I needed the HoldForm to prevent Mathematica from
automatically calculate the Numerator into the original number.

//Peter

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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