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

[M. F. Hasler]

 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).
>
> Is that right?  I think it would be a good idea to add comments to the 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
> >
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> >
>
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