[seqfan] Re: The name of A053810

[David Sycamore]



For me the Name is clear and a glance at the data is enough to confirm the intended meaning.  The part “..of prime numbers” of the definition is not redundant since if it were removed we would have just “Prime powers”, meaning that primes are being raised to powers but without being clear about what those powers (exponents) actually are (Without restriction on the exponents we get 
A000961). A053810 restricts the exponents to primes.

If a name change is required consider “Numbers p^k, where both p and k are prime.”

Best regards
David Sycamore.

> On 3 Nov 2023, at 14:00, 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.
> 
> Best regards
> 
> Felix
> 
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