[seqfan] Re: oddness of iterations of sigma()

[Max Alekseyev]

Based on b-file for A231484, we can claim that there are no such odd
numbers up to 5812687429488336721 ~= 5.8 * 10^18.
Max

On Tue, Nov 12, 2013 at 10:09 AM, Harvey P. Dale <hpd at hpdale.org> wrote:
>         In response to the first question, there are no such odd numbers up to 50 million.
>         Best,
>         Harvey
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Max Alekseyev
> Sent: Tuesday, November 12, 2013 8:59 AM
> To: seqfaneu
> Subject: [seqfan] oddness of iterations of sigma()
>
> Vladimir Letsko is unfortunate in his attempts to join SeqFan maillist.
> So he asked me to forward his question; please 'carbon copy' your replies to his email.
>
> ---------- Forwarded message ----------
> From: Letsko Vladimir <val-etc at yandex.ru>
> Date: 2013/11/12
>
>
> Hello SeqFans!
>
> Does anybody know the answer on some questions associated with A231484?
>
> 1. Does there exists an odd number n > 1 for which sigma(n),
> sigma(sigma(n)) and sigma(sigma(sigma(n))) are odd too?
>
> 2. Does there exists a number n > 1 such that sigma(sigma(sigma(n)))/n < 1.5?
>
> 3. Note that sigma(3^4) = 11^2. Does there exists another pair (p,r) such that p is prime, r > 1 and sigma(p^r) = q^s where q is prime and s > 1?
>
> Best regards,
> Vladimir Letsko
>
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