[seqfan] Re: Lists of sums

[M. F. Hasler]

Jonathan,
your table is oeis.org/A125624.
Tables with rows and columns of infinite length are called
 "infinite square arrays", and must be read by antidiagonals.
If you do so for your table (ignoring 0 and 1) you get
(2, 3, 4, 5, 6, 8, 7, 10, 9, 16,...) = A125624

The author intended to put your columns as rows but incorrectly entered
them by raising instead of falling antidiagonals,
as a result his table is not what he writes in Example but exactly yours
(but columns going down, not up)
cf. https://oeis.org/A125624/table

But indeed your "incremental row/col. sums" are not in OEIS.
I think you might add it, maybe calling it
"incremental sums of columns of A125624, as numbers n=2,3,4,... are added
in the respective column".
(and I think you could (even should) start with 0,1 which does not change
the rest of the sequence.)

- Maximilian

On Tue, Oct 22, 2019 at 6:29 AM jnthn stdhr <jstdhr at gmail.com> wrote:

> 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,...
> 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
>