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Re: Help with "If" statement within "Table"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90550] Re: [mg90500] Help with "If" statement within "Table"
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 12 Jul 2008 05:34:36 -0400 (EDT)
  • References: <200807110602.CAA03738@smc.vnet.net>

On 11 Jul 2008, at 15:02, Diana wrote:

> Folks,
>
> I am trying to write a small program to count the number of divisors
> of a number which have at least one coprime neighbor, and secondly the
> number of divisors which have two coprime neighbors, (one on each
> side).
>
> For example, the divisors of 60 are {1, 2, 3, 4, 5, 6, 10, 12, 15, 20,
> 30, 60}. 6 of the divisors have at least one coprime neighbor, and 5
> of the divisors have two coprime neighbors.
>
> In doing this, I have written the following statement. "n" is the
> number for which I am calculating divisors, and "A136164" is my first
> list, the of number of divisors in the "at least one neighbor" case.
> For some reason, A136164 is not updating when the "If" statement is
> executed within the "Table" statement. Can someone help me? Thanks,
> Diana M.
>
> Table[If[CoprimeQ[Divisors[n][[j]], Divisors[n][[j - 1]]] ||
>    CoprimeQ[Divisors[n][[j]], Divisors[n][[j + 1]]],
>   A136164[[n]] = A136164[[n]] + 1,], {j, 3,
>   Length[Divisors[n]] - 2}];
>


It's hard to tell what is wrong (if anything) because you do not tell  
us how you initialized A136164. But with the initialization
n = 60; A136164 = ConstantArray[0, 100];
your program certainly works fine.
  It is, however, rather inefficient.  There are many better ways to  
do this, for example:

OCN[n_] := Module[{k = Divisors[n], l}, l = Partition[k, 2, 1];  
Union[Flatten[Pick[l, CoprimeQ @@@ l]]]]

will return a list of divisors which have a coprime neighbour, so in  
your case:

OCN[60]
{1, 2, 3, 4, 5, 6}

(your program does not count 1 and 2).

Andrzej Kozlowski


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