- --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>

wrote:>

If my grandmother were alive...

she would say, "Pourquoi quelqu'un ne soigne pas?" ...

roughly translated ... "Why doesn't anyone care?" Phil? Chris?

> --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@>

an

> wrote:

> >

> > I posted it, but it didn't go.

> >

> > Look at the formula...

> > sigma(abundant#) = 2*sigma(perfect#) + associated Mp + 1

> > 28 = sigma(12) = 2*sigma(6) + 3 + 1 = 28

> > 120 = sigma(56) = 2*sigma(28) + 7 + 1 = 120

> > and 2016 = sigma(992) = 2*sigma(496) + 31 + 1

> > etc.

> >

> > If an infinite list of abundant numbers was somehow connected to

> > infinite list of perfect numbers or at least one odd perfect

> number,

> > then the list or singular odd perfect number would have to occur

> > before 1/2 of the abundant number by the above formula. All the

> odd

> > abundant numbers are a multiple of 945, and the first one doesn't

> > generate a perfect number before 1/2 of its value. So it won't

> ever

> > happen. Are you convinced?

> >

> > Bill

> >

> Another... 32640 = sigma(16256) = 2*sigma(8128) + 127 + 1 = 32640.

> I'm confident. Ramon... do you like the argument? It took me a

> while to believe it, but once I saw the formula... whoa! Bill

> - --- Bill wrote (in part):
>

When you start out with an assumption like this, the rest of your

> roughly translated ... "Why doesn't anyone care?" Phil? Chris?

>

> > > All the odd abundant numbers are a multiple of 945...

argument is suspect. You don't even have to look much further to

find that the second odd abundant number is 1575, which is

certainly not a multiple of 945.

In fact, there are odd abundant numbers not divisible by 3, 5, or 7.

Try the product of the primes from 11 to 149:

7105630242567996762185122555313528897845637444413640621 - --- In primenumbers@yahoogroups.com, "jbrennen" <jb@...> wrote:
>

You are right... I thought about the multiples of 945... and it's

> --- Bill wrote (in part):

> >

> > roughly translated ... "Why doesn't anyone care?" Phil? Chris?

> >

> > > > All the odd abundant numbers are a multiple of 945...

>

absurd...

look at the connection between abundant and perfect numbers when I

use the sigma function and the odd perfect number idea will disappear

...

sigma(abundant#) = 2*sigma(perfect#) + assoc. Mp + 1

sigma(4n) = 2*sigma(2n) + associated Mp + 1

sigma(2n) = 2*sigma(n) + associated Mp + 1

sigma(n) = 2*sigma(n/2) + associated Mp + 1

even if the form of an odd abundant# is not known... the odd perfect

number before it is...

typically when someone would investigates the abundant# linked to the

well known list of perfect numbers, they would see the first

equation... and then believe the last one and notice that an odd

perfect number was not possible... the odd perfect# couldn't be a

whole number. Look at the it's form. Also, the associated Mp is

derived by dividing out 2's from the perfect# until the prime is left

over... kinda like a modulo function or a new 'multilo' function.

the sigma function is tricky. I'm convinced implicitly. Bill

> When you start out with an assumption like this, the rest of your

> argument is suspect. You don't even have to look much further to

> find that the second odd abundant number is 1575, which is

> certainly not a multiple of 945.

>

> In fact, there are odd abundant numbers not divisible by 3, 5, or 7.

>

> Try the product of the primes from 11 to 149:

>

> 7105630242567996762185122555313528897845637444413640621

>