[seqfan] Re: New "metaperfect" number for A068978

[M. F. Hasler]

I don't think that we should edit contents of a-files submitted by someone
else. We wouldn't take a PDF or image file uploaded in the very same way
and modify it to add information, so why only for .txt files?

I think there are many example of a similar situation where the new
contributor would (or has) rather upload(ed) a new file, in addition to the
existing one. (With name and date.) (And in cases where just one new value
is found, there's often a comment like "(The list lacks ... and maybe other
values. - ~~~~)" right next to the link.

Especially if not only lines are added but indexing is changed or
suppressed. As others mentioned, it would make it impossible to refer to
"Yamanouchi's fourth value" or the like, and it might be desirable and
useful to do this.


- Maximilian


On Thu, Mar 28, 2024, 22:24 Neil Sloane <njasloane at gmail.com> wrote:

> Allan,
> >  Perhaps we should change the
> text of the entry so that this file is labeled "Other examples, not
> necessarily consecutive", and add my new discovery to it?
>
>
> Sounds good!  You can download the list from the entry, then add your
> value(s), and resubmit it.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Thu, Mar 28, 2024 at 8:34 PM Allan Wechsler <acwacw at gmail.com> wrote:
>
> > The sequence oeis.org/A007429 records the sum, over all divisors of n,
> of
> > sigma_1(n).
> >
> > Sigma_1 itself (oeis.org/A000203) records the sum of the divisors
> > themselves.
> >
> > This "nested sigma" calculation causes me to think of A007429 as the
> > "metasigma" function. Like sigma_1, it is multiplicative. The basis can
> > easily be seen to be the following:
> >
> > A007429(p^k) = p^k + 2 p^(k-1) + 3 p^(k-2) + ... + (k+1)
> >
> > where the coefficient and the exponent always add to k+1.
> >
> > This "sigma-like" function gives rise to an analog of the multiperfect
> > numbers, which I think of as "metaperfect". A number N is metaperfect if
> N
> > divides A007429(N). These numbers are recorded in oeis.org/A068978. The
> > entry gives the first 28 examples in the data, found by Benoit Cloitre,
> > Rick Shepard, and Giovanni Resta. A bit later, Hiroaki  Yamanouchi found
> > the next three, and recorded them in a B-file.
> >
> > Yamanouchi also found 168 more examples, for a total of 200, but was not
> > confident enough of their consecutivity to add them to the B-file;
> instead,
> > these 200 metaperfect numbers are listed in their own file.
> >
> > In the last hour, I found, essentially by hand, an example that
> Yamanouchi
> > missed: 930 284 109 364 500, which would fit between Yamanouchi's entries
> > 65 and 66. I'm not sure exactly what to do. Perhaps we should change the
> > text of the entry so that this file is labeled "Other examples, not
> > necessarily consecutive", and add my new discovery to it?
> >
> > I would also appreciate it if somebody could verify the validity of my
> new
> > example. Its factorization is 2^2*3^4*5^3*11^2*17*19*73*83*97, and I
> claim
> > it is "metaperfect" with order 14. (Because it is not divisible by 7, it
> > has a "partner" exactly 7 times bigger, which is also metaperfect, but of
> > order 18. This one is also not in Yamanouchi's list.)
>