[seqfan] Re: The name of A053810

M. F. Hasler oeis at hasler.fr
Mon Nov 6 14:16:11 CET 2023

```Also, the comment von JvP,

This is to triprimes as A053810 <https://oeis.org/A053810> (Prime powers of
prime numbers) is to primes and as semiprimes are to A113877
<https://oeis.org/A113877> (Semiprimes to semiprime powers). - Jonathan Vos
Post <https://oeis.org/wiki/User:Jonathan_Vos_Post>, Mar 26 2013

does not make sense when "this" is exactly A053810
<https://oeis.org/A053810> ...

- Maximilian

On Fri, Nov 3, 2023 at 11:15 AM Neil Sloane <njasloane at gmail.com> wrote:

> Dear Felix, Arthur:  Thank you for those comments about the meaning of
> "prime power".  I will try to deal with this matter in the next couple of
> days.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Fri, Nov 3, 2023 at 9:47 AM Arthur O'Dwyer <arthur.j.odwyer at gmail.com>
> wrote:
>
> > On Fri, Nov 3, 2023 at 9:00 AM Felix Fröhlich <felix.froe at gmail.com>
> > wrote:
> >
> > > Dear SeqFans,
> > > to me, the definition of A053810 sounds strange. The first comment in
> > > A000961 says "The term prime power is ambiguous. To a mathematician it
> > > means any number p^k, p prime, k >= 0, including p^0 = 1". This seems
> to
> > > suggest that the "... of prime numbers" part in the definition of
> A053810
> > > is redundant. The PARI code seems to suggest that the actual definition
> > is
> > > "Prime-th powers of prime numbers". Maybe the name could be written
> more
> > > clearly as "Prime powers with prime exponents", or, perhaps, "Powers of
> > > prime numbers with prime exponents".
> > >
> > > As this is an old sequence I want to discuss this possible change
> first.
> > >
> >
> > I think there are several defects in this area.
> > - A000961's first comment "The term prime power is ambiguous" is silly
> IMO.
> > "To a mathematician it means..." the thing it means, right? To a
> > non-mathematician, I don't think it means anything (and OEIS wouldn't
> care
> > about that meaning anyway). The first comment is adequately summarized in
> > the current title. But the second comment — that it's debatable whether 1
> > should count as a prime power — is useful, and in particular the fact
> > that A246655 is the same as A000961 without "1" needn't be a
> parenthetical.
> > - A053810's first comment "This is to triprimes..." is here by mistake;
> it
> > has been transposed from A217784 (where it belongs).
> > - A053810's actual title should be "Primes to prime powers," by analogy
> > to A113877 and A217784.
> > - Consider whether all three sequences' titles should have the word
> > "raised" added: "Primes *raised* to prime powers," "Semiprimes *raised*
> to
> > semiprime powers," "Triprimes *raised* to triprime powers." That might
> > lighten the heavy lifting currently being done by the small word "to".
> >
> > –Arthur
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```