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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90549] Re: Help with "If" statement within "Table"
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 12 Jul 2008 05:34:25 -0400 (EDT)

On 7/11/08 at 2:02 AM, diana.mecum at gmail.com (Diana) wrote:

>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?

I did not try to figure out why the code you posted didn't give
you the desired result. But here is a way to select all of the
factors that have at least one coprime neighbor.

In[18]:= factors = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60};

In[19]:= Pick[Rest@factors,
  CoprimeQ @@@ Partition[factors, 2, 1], True]

Out[19]= {2,3,4,5,6}

And this picks out all the factors that have a coprime on either side

In[20]:= Most@
  Pick[factors[[3 ;;]],
   And @@@ Partition[CoprimeQ @@@ Partition[factors, 2, 1], 2, 1],
   True]

Out[20]= {3,4,5}

Note, I intentionally excluded 1 from these lists. If one is to
be included then it should be on the first list and that means 2
should be included on the second list.


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