[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

Best regards

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>

> 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
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