# [seqfan] Re: Who understands Granville numbers?

Alonso Del Arte alonso.delarte at gmail.com
Thu Oct 28 16:54:14 CEST 2010

```I did read that comment, and I looked at the Maple program, and I thought
about how to rewrite it for Mathematica. But I am still confused, still
don't understand what the point of doing all those sums is. What does it
mean for a number to be in S besides having gone through some convoluted
test? What was it that motivated Andrew Granville to devise this complicated
test in the first place? Was he aiming to gain some insight towards finding
an odd perfect number?

How would you go about seeing if 30 is S-perfect? If none of its divisors
are S-perfect themselves, can we forget about 30 and move on to 31? But 28
is not divisible by any S-perfect numbers (6 or 24). And what about prime
numbers? What is the easiest way to explain their not being in this
sequence? Or with a number like 2989441, should we first look at its
smallest prime divisor or at its second largest divisor?

On Thu, Oct 28, 2010 at 4:12 AM, Vladimir Shevelev <shevelev at bgu.ac.il>wrote:

> About A118372. It seems very plausible that every term has the form
> a(n)=(2^k(n)-1)2^m(n) (maybe, this is known). If so, then there are at least
> 3 accompanying sequences which are not in OEIS:
>
> for 2^k(n)-1: 3 3 7 3 63 7 3 31 3 7 3 127...
> for k(n):        2 2 3 2   6  3 2  5  2 3 2    8...
> for m(n):       1 3 2 5   1  5 7  4  9 8 11  6...
>
> Regards,
>
> ----- Original Message -----
> From: Alonso Del Arte <alonso.delarte at gmail.com>
> Date: Thursday, October 28, 2010 1:10
> Subject: [seqfan]  Who understands Granville numbers?
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>
> > So I come across the concept of Granville numbers
> > (A118372<http://www.research.att.com/~njas/sequences/A118372>)
> > in Jean-Marie de Koninck's book *Those Fascinating Numbers*. But
> > the concept
> > is giving me a headache. Is the definition of the set S
> > recursive (one
> > having to do a complete divisor tree to figure out membership)
> > or am I
> > completely misunderstanding it? I've had an easier time doing my
> > taxes.
> > Al
> >
> > P.S. Daniel and I have signed up for a couple of slots for
> > Sequence of the
> > Day in November. Any SeqFan who hasn't yet chosen a Sequence of
> > the Day is
> > invited to sign up to choose it one day in November or December.
> >
> > _______________________________________________
> >
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> >
>