# [seqfan] Re: 1 is square (square of unit 1) but is not squareful (i.e. it is squarefree, no repeated primes in its prime factorization)

Charles Greathouse charles.greathouse at case.edu
Thu Aug 19 14:49:14 CEST 2010

```"Every prime factor repeated at least twice" is powerful:
http://mathworld.wolfram.com/PowerfulNumber.html
http://oeis.org/classic/A001694

Squareful is to be avoided, I think, in the OEIS because it can mean
nonsquarefree or powerful.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Aug 17, 2010 at 4:27 PM, Daniel Forgues <kephalopod at gmail.com> wrote:
> [http://mathworld.wolfram.com/Squareful.html]
>
> MathWorld defines squareful as not squarefree, but I would have
> preferred squaresome with that meaning and squareful to mean that
> every prime factor is at least repeated twice.  Similarly, cubesome
> would mean that at least one prime factor is repeated three times and
> cubeful would mean that every prime factor is at least repeated 3
> times. And so on...  But
>
> MathWorl defines a number as squareful if at least one of its prime
> factors is repeated... (seems unfortunately confusing...)
>
> --
>
> Daniel Forgues
>
>
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>

```

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