Re: Special Prime Product

• To: mathgroup at smc.vnet.net
• Subject: [mg53379] Re: [mg53363] Special Prime Product
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 8 Jan 2005 23:02:40 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200501080739.CAA17748@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Why are you surprised at the result?  After all, if n is even, then 2 is
a prime divisor of n and so one of the factors in the product you form
is (2 - 2)/(2 - 1).

So I'm assuming there is some error in your description of the product
you actually want.

Also, you made some typos:  You used lower-case "primeFactorList" within
the definitin of specpriprod; you need to use "PrimeFactorList".  And
expression that called it, you used "specprimprod".

In any case, I have a couple of recommendations.  First, why not follow
the Mathematica convention of meaningful names and name your function
specialPrimeProduct?  That way you might avoid the second of those typos.

Second, your definition needlessly invokes PrimeFactorList twice and
then needlessly indexes into it.  You could do the whole thing as
follows, making use of Mathematica's list-manipulation ability:

specialPrimeProduct[n_] :=
Module[{primes = PrimeFactorList[n]},
Times @@ (primes - 2)/(primes - 1)]

Of course if you are working with a really large n -- not the case at
all in your example -- then any advantage in efficiency of the above
code might be offset by use of a lot of memory to store temporarily the
entire list PrimeFactorList[n].

Gilmar wrote:
> I'm attempting to form a product:
> _____
> |  | (p-2)
> |  | -------
> |  | (p-1)
> p Prime, p|n
>
> I call the program:
>
> << NumberTheory`NumberTheoryFunctions`
> and use the function "PrimeFactorList" in it,  to build
> the following module:
>
> specpriprod[n_]:=
> Module[{v},v=Product[(primeFactorList[n][[i]]-2)/(primeFactorList[n][[i]]-2),
> {i,Length[PrimeFactorList[n]]}];v]
>
> specpriprod is an abbreviation for "Special Prime Product".
>
> When I evaluate:
> Table[{n,specprimprod[n]},{n,4,100,2}]
>
> I only get specprimprod[n] = 0 for n even between 4 and 100.
> Help! and Thank you for your help!
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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