Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90552] Re: Help with "If" statement within "Table"
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 12 Jul 2008 05:34:59 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g56t9c$3qo$1@smc.vnet.net>

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.

<snip>

I give you a functional approach to achieve what you are looking for. 
The function ccp (count coprimes} works with one and two coprime 
neighbors and can be easily modified to compute many of the integer 
sequences related to A136164 [1].

     ccp[n_Integer, neighbors_: 1] :=
      Module[{c, p},
       p = Partition[Divisors[n], neighbors + 1, 1];
       c = CoprimeQ[Sequence @@ #] & /@ p;
       Pick[p, c] // Flatten // Union // Length
      ]

     SetAttributes[ccp, Listable]

     ccp@Range[30]
     ccp[60]
     ccp[Range[30], 2]
     ccp[60, 2]

     {0, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 4, 2, 3, 3, 2, 2, 3, 2, 4, \
      3, 3, 2, 4, 2, 3, 2, 4, 2, 5}

     6

     {0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 3, 0, 3, 3, 0, 0, 3, 0, 0, \
      3, 3, 0, 3, 0, 3, 0, 0, 0, 4}

     5

[1] A136164, *The On-Line Encyclopedia of Integer Sequences*,
"a(n) = the number of divisors of n that are each coprime to the 
previous or the following divisor of n."

http://www.research.att.com/~njas/sequences/A136164

Regards,
-- Jean-Marc


  • Prev by Date: Re: Help with "If" statement within "Table"
  • Next by Date: Re: How to replace TextListPlot ?
  • Previous by thread: Re: Help with "If" statement within "Table"
  • Next by thread: Re: Help with "If" statement within "Table"