[seqfan] Re: Comments and corrections: A122811 and A059975
Alonso Del Arte
alonso.delarte at gmail.com
Fri May 21 18:12:30 CEST 2010
I agree wholeheartedly about A059975. The current name requires knowledge of
both complex multiplication and fast Fourier transforms to understand,
whereas "least number of prime factors (counted with multiplicity) of any
integer with n divisors" requires just basic number theory without reference
to the complex plane.
It's hardly an isolated occurrence in the OEIS, but that's understandable:
the original contributor may have been researching a very specific problem
and overlooked the more common, simpler situation in which the sequence
would arise. There are quite a few other similar situations throughout the
table.
Al
On Fri, May 21, 2010 at 10:51 AM, <hv at crypt.org> wrote:
> %N A122811 Number of prime factors (counted with multiplicity) of the
> smallest
> odd number with exactly n divisors.
> - add a comment with crossref, and correct repeated typo in crossrefs.
>
> %N A059975 n*a(n) is the number of complex multiplications needed for the
> fast
> Fourier transform of n numbers, writing n = r1 * r2 where r1 is a prime.
> - add comment and matching formula, with crossrefs.
>
> Replace:
> %F A122811 a(n) = Omega(A038457(n)), where Omega(n) = A001222(n).
> %Y A122811 Cf. A001222, A038457, A122376.
> with:
> %C A122811 This sequence first differs from A059975(n) at n=16, because
> 3^3.5.7 is less than 3.5.7.11.
> %F A122811 a(n) = Omega(A038547(n)), where Omega(n) = A001222(n).
> %Y A122811 Cf. A001222, A038547, A122376, A059975.
>
> Add:
> %C A059975 a(n) is the least number of prime factors (counted with
> multiplicity) of any integer with n divisors.
> %F A059975 a(n) = min(A001222(x): A000005(x)=n).
> %Y A059975 Cf. A001222, A000005.
>
> Arguably, this comment for A059975 might actually be a more natural name
> for the sequence.
>
> Hugo
>
>
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