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

John Machacek jmachacek.math at gmail.com
Sat May 9 05:30:17 CEST 2020

```Hi,

I believe it is iterates of phi, sigma, phi, phi, sigma, phi, phi, sigma,
phi,... until reaching 1 for each positive integer n=1,2,3,4.... When going
to the next integer we "skip" that integer and start with phi(n).

Here is A032452 split in this way.

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,...

Notice the first entry in each row is phi(n). The SageMath code below
reproduces A032452.

Best,
John

N = 10

n = 1

seq = []

while n < N:

a = euler_phi(n)

seq.append(a)

i = 0

while a != 1:

if i%3 == 0:

a = sigma(a)

else:

a = euler_phi(a)

seq.append(a)

i += 1

n += 1

On Fri, May 8, 2020 at 9:53 PM Neil Sloane <njasloane at gmail.com> wrote:

> All those sequences have a (free) link to the paper - see under the LINKS
> section!
>
> 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 7:51 PM Tom Duff <td at pixar.com> wrote:
>
> > Got it here: http://iq0.com/alaoglu-erdos-conjecture.pdf
> > It's only two pages.
> >
> > On Fri, May 8, 2020 at 4:28 PM Marc LeBrun <mlb at well.com> wrote:
> > >
> > > >=Neil Sloane
> > >
> > > Perhaps if someone has access to that Alaoglu & Erdös reference it
> might
> > help?
> > >
> > >
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```