# [seqfan] Re: Iterating sigma - 1

Robert G. Wilson v rgwv at rgwv.com
Fri May 7 05:45:43 CEST 2010

```Et al,

I wrote the following Mathematica program and tested all 1<n<10^6 and
the conjecture holds.

f[n_] := Plus @@ Divisors at n - 1;  g[n_] := NestWhile[f@# &, n, ! PrimeQ@#
&]; k = 2; While[k < 10^7, g at k; k++]

And for A039655  Number of iterations of f(x) = sigma(x)-1 on n required to
reach a prime.
h[n_] := Length at NestWhileList[f@# &, n, ! PrimeQ@# &] - 1; Table[h at n, {n, 2,
20}]

Sincerely yours, Bob.

--------------------------------------------------
From: <franktaw at netscape.net>
Sent: Thursday, May 06, 2010 4:51 PM
To: <seqfan at list.seqfan.eu>
Subject: [seqfan]  Iterating sigma - 1

> Consider http://www.research.att.com/~njas/sequences/A039654 - Prime
> reached by iterating f(x) = sigma(x)-1 on n.
>
> It isn't obvious that this iteration always reaches a prime, although
> it seems nearly certain that it does. Should we add something like ",
> or 0 if no prime is ever reached", with a comment that apparently the
> sequence always does reach a prime? (Or can someone prove that a prime
> is always reached?)
>
> One might, in this case, also add a(1) = 0 (suitably modifying the
> comment).
>
> Franklin T. Adams-Watters
>
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/

```