# [seqfan] Re: The name of A053810

Neil Sloane njasloane at gmail.com
Fri Nov 3 16:14:26 CET 2023

```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/
>
```