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Non-prime

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  • Samir Musalı
    We say that primes must have only 2 divisors. In other hand, if number has 2 divisors, it s prime. 2 is also prime and the first element and only even element
    Message 1 of 2 , Feb 4, 2012
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      We say that primes must have only 2 divisors. In other hand, if number has
      2 divisors, it's prime.
      2 is also prime and the first element and only even element of prime set.
      What must we name the numbers which have 3 or 5 or 7 or... divisors? It can
      be interesting to think about these.

      As we know, 6, 28, ... are perfect numbers.

      But let's think:
      any a natural number has a[1], a[2], ... , a[n] divisors. Clearly, we see
      a[n]=n;
      if a[1]+a[2]+...+a[n-1]=a then a-->perfect number.
      if a[1]*a[2]*a[3]*...*a[n-1]=a then a--> ?

      after some tests, we can see if a[1]*a[2]*...*a[n-1]=a then absolutely,
      n=3... a has 3 divisors.

      *Question: is there any a natural number that:
      1) it has more than 3 divisors;*
      *2) a=a[1]*a[2]*a[n-1]....?*
      *
      *
      *
      *


      [Non-text portions of this message have been removed]
    • djbroadhurst
      ... Then a is either a product of distinct primes or the cube of a prime. David
      Message 2 of 2 , Feb 4, 2012
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        --- In primenumbers@yahoogroups.com,
        Samir Musalı <applied.samir@...> asked:

        > if a[1]*a[2]*a[3]*...*a[n-1]=a then a--> ?

        Then "a" is either a product of distinct primes
        or the cube of a prime.

        David
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