[seqfan] Re: Seqfan Digest, Vol 33, Issue 7

[Peter Lawrence]

Richard,
                does it help to know that

A(2^k*d) = A(d)        for odd d by definition
A(d) = 2^k*d + 1       is what we're trying to prove does not ever  
happen for odd d
                                     the right hand side is obviously  
odd,  but

A(d) for an odd d will be odd IFF d is a square   <---

in other words does your technique get any easier for

1 prime)      2^i
2 primes)    2^i * p^(2*j)
3 primes)    2^i * p^(2*j) * q^(2*k)
4 primes     etc...


-Peter Lawrence.


> ------------------------------
>
> Message: 3
> Date: Sun, 19 Jun 2011 20:33:34 +0200
> From: Richard Mathar <mathar at strw.leidenuniv.nl>
> To: seqfan at seqfan.eu
> Subject: [seqfan] Re: number theory question about A000593
> Message-ID: <201106191833.p5JIXYxb024098 at dommel.strw.leidenuniv.nl>
> Content-Type: text/plain; charset=us-ascii
>
>
> The conjecture concerning the sums of odd prime divisors of n  
> arising in
> http://list.seqfan.eu/pipermail/seqfan/2011-June/015003.html
> can be verified for all cases where n has at most 3 distinct prime  
> divisors.
> I generated a script that intends to show why this is correct in these
> simple cases, http://www.strw.leidenuniv.nl/~mathar/progs/ 
> a000593.pdf .
>
> Richard Mathar
>
>
> ------------------------------