       Re: Special Prime Product

• To: mathgroup at smc.vnet.net
• Subject: [mg53381] Re: Special Prime Product
• Date: Sat, 8 Jan 2005 23:02:43 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```On 1/8/05 at 2:39 AM, gilmar.rodriguez at nwfwmd.state.fl.us (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.

But for any even number 2 will be a prime factor. That means p-2 evaluates to zero and the product must be zero. So, there is no apparent problem with the results.

I do note your code could be improved and will not do what you describe as written. You are using primeFactorList instead of PrimeFactorList and you have p-2 in the demonimator. Also, you do not need the local variable v.

A better approach would be

specpriprod[n_]:=
Module[{p = PrimeFactorList[n]},
Product[(p[[i]]-2)/(p[[i]]-1),{i,Length[p]}]]

And even easier to read and probably more efficient is

specpriprod[n_]:=
Module[{p = PrimeFactorList[n]},
Times@@((p-2)/(p-1))]
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```

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