[seqfan] Re: A079277 review

David Wilson davidwwilson at comcast.net
Mon Feb 27 02:55:10 CET 2012


I didn't delete anything, and I wouldn't without permission, ergo the post.

On 2/26/2012 5:21 PM, Neil Sloane wrote:
> I care a lot.
>
> Please don't delete anything in the OEIS just because you don't understand
> it.
>
> Let me repeat that:
>
> Please don't delete anything in the OEIS just because you don't understand
> it.
>
> The idea that future editors will start deleting parts of old sequences
> because
> they don't understand them fills me with horror.
>
> I added some specific further comments below.
>
> Neil
>
> PS Having said that, I agree that this entry
> needs editorial work. But use a fine brush, not a sledgehammer.
>
>
> On Sun, Feb 26, 2012 at 4:04 PM, David Wilson<davidwwilson at comcast.net>wrote:
>
>> I am reviewing A079277 in relation to some other sequences I added not
>> long ago.
>>
>> There is a monolithic comment which I have broken into its five
>> constituent pieces:
>>
>> *[0)] The function a(n) complements Eulers phi-function:*
>>
>> The meaning of this comment is unclear, perhaps it was meant to be
>> clarified and supported by subsequent comments involving phi, but I don't
>> think they do, as I note later. I vote to elide this comment.
>>
>>
> NO PLEASE LEAVE IT!  It is an interesting comment.
>
>
>> *1) a(n)+phi(n)=n if n is a power of a prime.*
>>
>> Technically true, but phi(n) takes on a special form on prime powers:
>> phi(p^e) = (p-1)*p^(e-1), so this really just says a(p^e) = p^(e-1) in an
>> obfuscatory fashion. Perhaps we should replace this comment with "a(p^e) =
>> p^(e-1) for prime p and e>= 1". The relationship between a(n) and phi(n)
>> on prime powers n says little about a relationship on general n, so this
>> statement doesn't really support comment 0.
>>
>> *2) It seems also that a(n)+phi(n)>=n for "almost all numbers".*
>>
>> This comment is vague. If I take it to mean n satisfying a(n) + phi(n)>=
>> n have density 1 on the positive integers, I cannot prove it.  However, I
>> can find an (almost certainly) infinite number of counterexamples,
>> including any number n = pq with primes p, q satisfying p^2-p+1<  q<  p^2,
>> the smallest being n = 115. These counterexamples take the wind out of
>> comment 0. This comment scores low on clarity, truth, and relevance, and I
>> vote to elide it.
>>
> PLEASE DON'T
>
>> *3) a(2n)=n+1 if and only if n is a Mersenne prime.*
>> *4) Lim a(n^k)/n^k =1 if n has at least two prime factors and k goes to
>> infinity.*
>>
>> These comments are true and should remain (on separate lines).
>>
>> Agree? Disagree? Care?
>>
>>
>>
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>>
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>
>




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