A124184: prime factorization of 1?

[franktaw at netscape.net]

It's not really controversial, it's just that many people don't have a 
clear understanding of it.  If you look at the complement of A124184, 
you get something like "positive integers divisible by one or more of 
their own prime factorization exponents".  Since 1 doesn't have any 
such exponents, it isn't divisible by any of them, so it is not in the 
complement of A124184.  That means it is in A124184.

On the other hand, there are numerous cases in the OEIS where 1 is 
treated arbitrarily for factorization purposes.  For example, A027746 - 
the table of prime factors with repetition - has an initial 1, which 
really should not be there.

Franklin T. Adams-Watters


-----Original Message-----
From: qq-quet at mindspring.com

Zak Seidov wrote:

>Dear seqfans,
>
>In A124184,
>shouldn't we omit 1
>(I omit it, while Leroy includes)?
>
>What is prime factorization of 1?
>...


I SHOULD have included a comment that the 1 case is controversial.
Someone might argue that, since 1 has no prime factors and therefore
hasn't any (positive) prime-factorization exponents, then none of 1's
prime-factorization exponents divide 1.
;)
(And so, technically, 1 meets the definition of the sequence....sort 
of..)


So I included the 1 in the event someone searching for this sequence on
the OEIS includes a 1 at the beginning of the sequence they are 
searching
for.


Thanks,
Leroy Quet



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