[seqfan] Re: A079277 review

Neil Sloane njasloane at gmail.com
Sun Feb 26 23:21:08 CET 2012

I care a lot.

Please don't delete anything in the OEIS just because you don't understand

Let me repeat that:

Please don't delete anything in the OEIS just because you don't understand

The idea that future editors will start deleting parts of old sequences
they don't understand them fills me with horror.

I added some specific further comments below.


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.


> *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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Dear Friends, I will soon be retiring from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

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