# [seqfan] Re: defn of A032452 transients in modified Poulet

Neil Sloane njasloane at gmail.com
Fri May 8 19:40:49 CEST 2020

```Richard

I tried assuming that "sigma" mean the aliquot sigma, sum of divisors < n,
but I still do not understand A032452.

Since phi(6) = phi(4) = 2, it follows that phi(phi(7))=2, phi(phi(8))=2 so
whatever the offset and no matter which version of sigma we use, we should
get a(7)=a(8).  But her sequence
starts 1,1,2,3,2,1,2,3,2,1,4,7,6,2,3,2,1,2,3,2,.. and there are no two
equal consecutive entries.
So maybe this is NOT the length of the transient.

Here is the original submission, which she submitted via an html "form",
which was processed by my cgi-bin shell program on our external machine,
which then composed an email to me and was sent through the firewall to my
local machine:

>From njas at akpublic.research.att.com  Tue Apr  7 07:57:08 1998
To: njas at research.att.com
Date: Tue, 7 Apr 1998 07:56:31 -0400 (EDT)
From: "N. J. A. Sloane" <njas at research.att.com>
Subject: SEQ FROM Ursula Gagelmann

%I A000001
%S A000001
1,1,2,3,2,1,2,3,2,1,4,7,6,2,3,2,1,2,3,2,1,6,12,4,2,3,2,1,4,7,6,2,3,2,1,6,12,4,2,3,2,1,4,7,6,2,3,2,1,10,18,6,2,3,2,1,4,7,6,2,3,2,1,12,28,12,4,7,6,2,3,2,1,6,12,4,2,3,2,1
%N A000001 iterates phi,phi,sigma,phi,phi,sigma,...
%D A000001 Alaoglu & Erdös:  A conjecture...  Bull Amer Math Soc 50 (1944),
881-882
%D A000001
%D A000001
%H A000001
%H A000001
%H A000001
%F A000001
%C A000001
%Y A000001
%A A000001 Ursula Gagelmann (gagelmann at altavista.net)
%O A000001 0
%K A000001 ,nonn,

So this is still a mystery.

It is quite possible she is still living in Germany - could you try
contacting her?

<https://www.dr-gagelmann-schriesheim.de/>
Dr. med. Ursula Gagelmann (Psychologist) in 69198 ...
en.doctena.de › Dr_med_Ursula_Gagelmann-343245 › Pr...
<https://en.doctena.de/doctor/Dr_med_Ursula_Gagelmann-343245/Praxis_Frau_Dr_med_Ursula_Gagelmann-297597>
Schedule an appointment online with Dr. med. Ursula Gagelmann,
Psychologist. Also phone number, opening hours, education, awards,
recommandations and ...

Dr. med. Ursula Gagelmann (Ärztin) in Schriesheim | jameda
www.jameda.de › aerzte › uebersicht
<https://www.jameda.de/schriesheim/aerzte/psychosom-med-u-psychotherapeuten/dr-ursula-gagelmann/uebersicht/80335796_1/>

1.
2.

Dr. med. Ursula Gagelmann (Ärztin) in Weinheimer Str. 1 B, 69198
Schriesheim ✓ Das sagen Nutzer über Dr. Gagelmann ✓ Finden Sie mehr zu Dr.
Gagelmann!

Bewertung & Infos Frau Dr. med. Ursula Gagelmann
www.weisse-liste.de › ... › Arztsuche
<https://www.weisse-liste.de/de/arzt/arztsuche/ergebnisliste/profil/;jsessionid=ED4E57815896E75A677F1C98CCD58901?distance=2622&id=1159941&type=medic>

1.

Alle Infos zur Praxis von Frau Dr. med. Ursula GagelmannSpezialist für
Psychotherapeutische Medizin. Bewertungen ansehen oder Ärztin selbst
bewerten.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Fri, May 8, 2020 at 1:16 PM Neil Sloane <njasloane at gmail.com> wrote:

> Richard,
> I found the original submissions from Ursula Gagelmann from 1998.
> For A032450 there was a formula that I have now added to the entry (I see
> you also added a comment - presumably saying the same thing, I did not have
> time to check).
>
> For A032452 unfortunately there is nothing more than what I put in the
> entry for the sequence (except the submission date, which I have now added)
> She definitely says the offset is 0. However, that does not mean anything
> since  0 was the default offset and she did not change it in any of her
> half-dozen submissions at that time.  Perhaps she did not understand the
> significance of the offset.
> So it is very likely the offset in A032452 should be 1 not 0.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Email: njasloane at gmail.com
>
>
>
> On Fri, May 8, 2020 at 11:32 AM Richard J. Mathar <mathar at mpia-hd.mpg.de>
> wrote:
>
>> It would be nice to have a definition of a(n) in terms of n in A032452
>> (modified Poulet sequences).
>> Starting at n, we have the sequences
>> [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
>> [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
>> [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
>> [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
>> [5, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
>> [6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
>> [7, 6, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
>> [8, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
>> [9, 6, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
>> [10, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...]
>> [11, 10, 4, 7, 6, 2, 3, 2, 1, 1, 1,...]
>> [12, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...]
>> [13, 12, 4, 7, 6, 2, 3, 2, 1, 1, 1,...]
>> ...
>> if we iterate twice phi(.) and once sigma(.) on the elements in these
>> sequences.
>> I suspect that a(n) is somehow a cumulation of periods or their
>> transients,
>> similar to A032450, but cannot find how that might actually be realized
>> in A032452.
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
```