# [seqfan] Re: 2^n - 2

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Sat Apr 11 18:54:34 CEST 2009

```I just submitted this sequence. Can someone answer the question in the comment line?

%I A159353
%S A159353 1,1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,10
%N A159353 a(n) = the smallest positive integer such that a(n) *(2^n -2) is a multiple of n.
%C A159353 This is not the same sequence as sequence A032742, where A032742(n) = the largest proper divisor of n. For which n do the sequences A032742 and A159353 differ?
%Y A159353 A000918
%K A159353 more,nonn
%O A159353 1,4

Thanks,
Leroy Quet

--- On Sat, 4/11/09, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
> Subject: [seqfan] Re: 2^n - 2
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Saturday, April 11, 2009, 4:38 PM
>
> Never mind. Poulet numbers, which are composite, will have
> an a(n) of 1, which is not their greatest proper divisor.
>
> Yes, it was a dumb question.
>
> Sorry, thanks,
> Leroy Quet
>
> --- On Sat, 4/11/09, Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
> wrote:
>
> > From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
> > Subject: [seqfan]  2^n - 2
> > To: seqfan at seqfan.eu
> > Date: Saturday, April 11, 2009, 4:32 PM
> >
> > Let a(n) be the smallest positive integer such that
> > a(n)* (2^n - 2) is divisible by n.
> >
> > This is probably a dumb question, but is
> > {a(k)} the same as sequence A032742, where A032742(n)
> = the
> > largest proper divisor of n?
> >
> > Thanks,
> > Leroy Quet

```