Re: odd perfect number
- --- In email@example.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...
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: