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

>> Look at the formula...

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

>

> First time I see it. Is it a result of yourself? Do you have a proof?

1) Obviously, if A is even perfect number, it must be of the form

A = 2^(n-1)*M_n, where M_n = (2^n - 1) is a Mersenne prime. The proof is

straightforward, see

http://primes.utm.edu/notes/proofs/EvenPerfect.html.
Then, sigma(A) = 2^n*M_n and sigma(2A) = (2^(n+1) - 1)*2^n = 2*sigma(A) +

(2^n-1) + 1.

So, the formula holds for abundant numbers equal to twice-an-even-perfect.

2) There are -way- too many abundant numbers which are NOT of the form

2*perfect number. 18, 20, ... The formula does not (and also -can- not)

hold for them.

> If you have it, I bet it involves even perfect numbers (because of that

> Mp), so why do you expect it to be applicable to odd perfects?

In fact... WHAT exactly is "associated Mp" in the case of odd perfect

numbers?

Peter

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[Name] Peter Kosinar [Quote] 2B | ~2B = exp(i*PI) [ICQ] 134813278