Problems with A000028/A000379.

[wouter meeussen]

hi Tony et al.,

I just checked my backup CD's, but could not retrace the original mails.
What I remember is this:

at some stage in september 2001, I (was hinted to) hit on a "Infinitary"
lode, going from divisors, over
iSigma, iMoebiusMu, then iEulerPhi, and finally iZeta.

It seems that A049417, then A064175 (with reference to Lambek & Moser
included: superseeker hit?)
define the time frame.

In 2001, I mailed to Neil S. with a request for help on A000028, which was
rather obscure (to me) and short at the time. As I remember (??) Neil
reacted by 'correcting' the A000028 and A000379, but I don't remember how,
or what problem I posed about'm. I never understood what they originally
were supposed to be, by lack of  copy of that original reference (despite my
nagging, Neil isn't a library on his own...).

What were the original versions? You still seem to have them.
What is all the "amazing ~ unamazing" about?

When I think of those "infinitary" items, I remember them as examples where
the difference with the "ordinary" divisors-sigma-mu-phi-Zeta stuff only
starts to show up at rather high indices. I mentioned this in A064179:
" mu[45]=0 but iMoebiusMu[45]=1 because 45 = 3^2 * 5^1 and the binary digits
of 2 and 1 add up to 2, an even number."
and in A064175:
" mu[60]=0 but iMoebiusMu[60]=-1 because 60 = 2^2 *3^1 *5^1 and the binary
digits of 2 and 1 and 1 add up to 3, an odd number."
I can also check the mail archives at work, (after new year, not now), and
see if I can trace the correspondence with Neil from there.

But ok now, let's get it right this time.

season's greetings,

Wouter.



----- Original Message ----- 
From: "T. D. Noe" <noe at sspectra.com>
To: <wouter.meeussen at pandora.be>
Sent: Thursday, December 20, 2007 5:56 PM
Subject: Fwd: Re: Problems with A000028/A000379.


> >I looked at sequence M0520, which became A000028, in the 1995 book form
of
> >OEIS.  There the sequence starts the same as A064175 -- it has the
> >"amazing" property.  Maybe the sequence was incorrectly modified sometime
> >after 1995.  So the comment in A000028 was correct in the past.
>
> You made a change to A000028 on Sept 10, 2001.  Do you have a record of
the
> changes?
>
> Best regards,
>
> Tony
>
>
>
> __________ NOD32 2738 (20071220) Informatie __________
>
> Dit bericht is gecontroleerd door het NOD32 Antivirus Systeem.
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>
>




Dear Seqfans:

Thanks to everyone who contributed to this discussion.
Indeed, the original definitions of A000028 and A000379
have somehow been corrupted over the years.
I have restored the original definitions, added Maple
programs, and recomputed the entries and the b-files.

The definition given for A000028 that was there until
an hour ago was:

%N A000028 A 2-way classification of integers: a(1) = 2, a(2) = 3, and for n > 2, a(n) is smallest number > a(n-1) not of the form a(i)*a(j) for 1 <= i < j < n.

This is not the right definition of A000028 and has now been replaced.

I have not been following the discussion about these sequences very
closely.  Now that A000028 and A000379 have been corrected,
perhaps members of the list can suggest what further changes

Best regards

Neil