[seqfan] Re: tau and sigma

[Frank Adams-Watters]

tau(n), sometimes called d(n) or sigma_0(n), is the number of divisors of n.
sigma(n), sometimes called sigma_1(n), is the sum of the divisors of n.

Franklin T. Adams-Watters

-----Original Message-----
From: Allan Wechsler <acwacw at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Mon, Aug 31, 2015 12:24 pm
Subject: [seqfan] Re: tau and sigma


My first guess at the meanings of tau() and sigma() were wrong; perhaps a
little
more context would be good.

On Fri, Jul 31, 2015 at 9:16 AM, Frank
Adams-Watters <franktaw at netscape.net>
wrote:

> Is the sequence of all numbers n
with tau(n+1) = tau(n-1) and sigma(n-1) =
> sigma(n+1) in the database? Likewise
for the second one? I'm not sure
> either of those should be accepted, but don't
even consider adding  a
> sequence "primes with property P" unless "numbers with
property P" is
> already there, or at the very least is submitted at the same
time.
>
> (Of course, this doesn't apply if P is really only applicable to
primes,
> e.g. if it involves primitive roots.)
>
> Franklin T.
Adams-Watters
>
> -----Original Message-----
> From: юрий герасимов
<2stepan at rambler.ru>
> To: seqfan <seqfan at list.seqfan.eu>
> Sent: Fri, Jul 31,
2015 1:07 am
> Subject: [seqfan] tau and sigma
>
>
>
> Dear SeqFans,
>
> 919,
13333097, 13358407, 70779463, 105125921, 110495719,
> 292840063, 321860263,
415520359, 617684959, 628112717, 993590681,...
>
> --> primes
> p satisfyng
tau(p + 1) = tau(p - 1) and sigma(p + 1) = sigma(p - 1);
>
> 53,
> 20543, 47843,
32003407, 59808803, 96144127, 113561243, 238818893,
> 1020720293,
> ...
>
> -->
primes p satisfyng tau(p + 2) = tau(p - 2) and sigma(p + 2) = sigma(p -
>
2).
>
> 1-th sequence or 2-th sequence is of general interest?
>
> Thanks.
>
JSG.
>
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