# [seqfan] Re: Help needed in checking terms in A259349

Tue Jul 18 18:18:45 CEST 2023

```See A001221. This meaning is well-established in the OEIS. At most, I would add a reference to that sequence.

On Monday, July 17, 2023 at 08:54:23 PM CDT, Neil Sloane <njasloane at gmail.com> wrote:

The English sentences are ambiguous.

"N has exactly 6 distinct prime factors"  according to you would permit
2^10*3*5*7*11*13, right?  But most people would say that 2^10*3*5*7*11*13
has 15 prime factors, and they are not all distinct.

Put it another way: how many prime factors does 8 have?  I say 3, and they
are not all distinct.

How many distinct prime factors does 8 have?  One answer is ONE, namely 2.
Another answer is ZERO, because 2 is a prime factor of 8 but it is not a
distinct prime factor.

So both sequences need comments explaining what the definitions really are,
and they need examples.

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com

On Mon, Jul 17, 2023 at 9:36 PM M. F. Hasler via SeqFan <
seqfan at list.seqfan.eu> wrote:

>  N has exactly 6 distinct prime factors <=> omega(N) = 6
>
> N is the product of exactly 6 distinct primes <=> omega(N) = bigomega(N) =
> 6
>
>
>
> On Mon, Jul 17, 2023, 20:50 Neil Sloane <njasloane at gmail.com> wrote:
>
> > I'm confused!  The new A364265 talks about numbers  "each with exactly 6
> > distinct prime factors."  Let the prime factorization of n be
> > Product_{i=1..k}  p_i ^ e_i.  The new sequence seems to say that there
> are
> > exactly six p_i's with e_i = 1, but there can also be other primes that
> > have e_i > 1. So k >= 6.
> >
> > Whereas for the original version,  we require that there are exactly six
> > p_i's with e_i = 1, and no other primes (so k = 6).
> >
> two
> > sequences explaining this.
> >
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Mon, Jul 17, 2023 at 4:28 PM Richard J. Mathar <mathar at mpia-hd.mpg.de
> >
> > wrote:
> >
> > > To fill the gap between A259349 (triples of consecutive
> square-free-free
> > > small-omega=6)
> > > and simpler sequence I've started A364265 (triples of consecutive
> > > small-omega=6).
> > >
> > > Richard Mathar
> > >
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
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```