## Non-prime

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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
Message 1 of 2 , Feb 4, 2012
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]....?*
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• ... Then a is either a product of distinct primes or the cube of a prime. David
Message 2 of 2 , Feb 4, 2012