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What Is a Composite Number With No Co-Prime Factors?

  1. Jan 26, 2015 #1
    I have come across a question in my explorations of recursive tilings using Gaussian and Eisenstein Integers. It seems there might be a class of composite numbers which have no factors (divisors) that are co-prime. So, for instance: 10 is composite, but its factors (2 and 5) are co-prime. The same is true for 6 and 12. However, 4, 8, 9, 16, 25 do not have factors which are co-prime. (I am including composite numbers with only one factor in this list). These are then examples of the class of numbers I am looking to identify.

    Without going into the details and reasoning for asking this question (unless it helps in finding the answer), I am initially curious if such a class of composites have been identified, and if so, perhaps there may be some significance that can shed some light on my problem.

    Any insights, thoughts?

  2. jcsd
  3. Jan 26, 2015 #2

    Stephen Tashi

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  4. Jan 26, 2015 #3
    Thanks Stephen,

    I think your suggestion is helping me to converge on the answer, although I clearly said that I am looking at composite numbers only. However I think that if I take the series pointed out (sequence A246655 in OEIS), and strip out all the primes, I will have the set I am looking for :)

    My intuition tells me that this is right because fractals (as I am exploring them with tilings in lattices) obey power laws.

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