[seqfan] Re: Lists of sums

[jnthn stdhr]

OK.  These are now  A328637 and A328638.

Maximilian, I added the name you suggested for the first sequence but
realized that A125624 doesn't have a 1 (or 0) in its first column, so the
name isn't quite right.  Also, per David's suggestion, maybe the zero
should be dropped so the sequence has offset 1 and conforms to the usual
list offset?

David, thanks for the name suggestion for the second sequence.  For now I
added a(0)=0 in order to be consistent with the first sequence , but that
will likely change.

-Jonathan

On Tue, Oct 22, 2019 at 1:30 PM David Seal <david.j.seal at gwynmop.com> wrote:

> I can offer a succinct definition of your second sequence: a(1) = 1, a(n)
> is the sum of m such that 2 <= m <= n and GPF(m) = GPF(n), where GPF(i) is
> the greatest prime factor of i (A006530).
>
> Best regards,
>
> David
>
>
> > On 21 October 2019 at 20:24 jnthn stdhr <jstdhr at gmail.com> wrote:
> >
> >
> > Hi folks.
> >
> > I will add either, or both, of these, if of interest.  Name suggestions
> > would be helpful, in that case.
> >
> > a(n) = 1, 3, 6, 4, 11, 10, 18, 8, 17, 20, 29, 12, 42, 34, 32, 28, 59,...
> >
> > Superseeker yields a blank stare.
> >
> > Here's what I did:
> >
> > If n = 0, 1, or a prime, start a column.  For each composite, find the
> > largest prime factor p and place n in column "p."
> > a(n) is then the sum m of all numbers in the same row as m.
> >
> > At n=20 it looks like this:
> >
> >                   18
> >            16   12  20
> >             8    9    15
> >             4    6    10   14
> > 0    1    2    3    5     7    11   13  17  19
> >
> > Summing columns as we go gives:
> >
> > a(n) = 0, 1, 2, 3, 6, 5, 9, 7, 14, 18, 15, 11, 30, 13, 21, 30, 17,...
> >
> > Also not in the database.
> >
> > -Jonathan
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>