Sorry,... the formula should have been posted as... (3^(2n-2))*(3^(2n-1)-1)/2. I thought about it while driving home last night. This idea follows from...
18345
Jose Ramón Brox
ambroxius
Sep 2, 2006 2:09 am
... From: "leavemsg1" <leavemsg1@...> ... A = 3^(2n-2), B = (3^(2n-1)-1)/2 N = A·B Sigma is a multiplicative function, and B = = 1 (mod 3), which...
18346
leavemsg1
Sep 2, 2006 7:23 pm
... implies CGD(A,B) = 1, so ... (B) = 2A ... Forget my attempt to formalize a formula for an odd-perfect number be- cause by your very sigma definitions......
18347
Jose Ramón Brox
ambroxius
Sep 2, 2006 9:36 pm
... From: "leavemsg1" <leavemsg1@...> ... Why is that so? If you have a sound argument for that idea, i.e., that the first perfect number must occur at...
18348
Roahn Wynar
hahahahastay...
Sep 3, 2006 1:10 am
As part of a project to generate some computer art and to build a video game, it came to pass that I needed a way to convert whole numbers into graphic images....
18349
Phil Carmody
thefatphil
Sep 3, 2006 7:12 am
... It's pretty cool. The idea of creating bijections between numbers and multi-dimensional images is one I've theorised about a lot (I was going to turn DeCSS...
18350
Chris Caldwell
primemogul
Sep 4, 2006 4:57 am
... Very nice. I wrote a script to draw some of these and see why you chose to work with the largest factor first (though I used a green square instead of a...
18351
Phil Carmody
thefatphil
Sep 4, 2006 4:29 pm
I don't suppose anyone can sketch a proof of it, could they? A quick search on the interweb failed to yield anything, and I don't remember seeing it in any of...
18352
Ignacio Larrosa Ca...
ilarrosa
Sep 4, 2006 6:15 pm
Monday, September 04, 2006 6:21 PM [GMT+1=CET], ... I think there are two or more versions of the theorem, related I suppose. In "Introduction to Analytic...
18353
Roahn Wynar
hahahahastay...
Sep 4, 2006 6:33 pm
For those who are interested, you can now experiment with the Whole Number Hash Applet at https://home.comcast.net/~rwynar/. You can input some pretty big...
18354
Phil Carmody
thefatphil
Sep 4, 2006 6:55 pm
... Many thanks Ignacio! The formulation of the theorem I have seen was different, but closely related (namely the C(2p-1,p-1) one), and hopefully not too much...
18355
Phil Carmody
thefatphil
Sep 4, 2006 8:54 pm
... Oh dear, you seem to have fallen for the "write once, run anywhere" bu^Wmarketting message that Sun was so proud of. Alas, it don't work here, and yes,...
18356
leavemsg1
Sep 4, 2006 10:47 pm
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 =...
18357
Chris Caldwell
primemogul
Sep 4, 2006 11:36 pm
... I'd wondered if you did that on purpose. Go to http://www.utm.edu/staff/caldwell/preprints/temp/ 1to30 is just that, 1, 2, 3, ... Then the flat primes p,...
18358
leavemsg1
Sep 5, 2006 5:45 pm
... number, ... odd ... ever ... Another... 32640 = sigma(16256) = 2*sigma(8128) + 127 + 1 = 32640. I'm confident. Ramon... do you like the argument? It took...
18359
Tuch
vr_aman
Sep 6, 2006 9:38 am
* Regards Raman / Tuch ... Here's a new way to find what you're looking for - Yahoo! Answers Send FREE SMS to your friend's mobile from Yahoo! Messenger...
18360
Tuch
vr_aman
Sep 6, 2006 9:45 am
Do you know any factor of 2^65537-1? I know M8191 has factor 338193759479 M131071: 231733529 M524287: 62914441 M2147483647: 295257526626031 * * * * Regards ...
18361
leavemsg1
Sep 6, 2006 3:21 pm
I wrote to Dr. Math on 9/6/06... today. He asked... What is your question? I wrote: I see the many definitions that math books are filled with and ponder- ed...
18362
leavemsg1
Sep 7, 2006 1:20 am
... ponder- ... the ... ...omit the restriction. The function should have been f(1/a + bi) = a * g(1+abi) ... it. ... de- ... real ... my ... made ... the ... ...
18363
leavemsg1
Sep 8, 2006 4:35 pm
... If my grandmother were alive... she would say, "Pourquoi quelqu'un ne soigne pas?" ... roughly translated ... "Why doesn't anyone care?" Phil? Chris? ... ...
18364
jbrennen
Sep 8, 2006 6:30 pm
... 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...
18365
Jose Ramón Brox
ambroxius
Sep 8, 2006 9:20 pm
[I tried to send this email several times these days. I hope this is the good one] ... First time I see it. Is it a result of yourself? Do you have a proof? If...
18366
Peter Kosinar
pkosinar
Sep 9, 2006 4:57 pm
... 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,...
18367
Jose Ramón Brox
ambroxius
Sep 9, 2006 7:37 pm
... I was aware of that. I was just asking for a proof of the claim as it was first stated, involving all perfect numbers (even the theoretical odd ones!). I'm...
18368
leavemsg1
Sep 10, 2006 2:30 pm
... You are right... I thought about the multiples of 945... and it's absurd... look at the connection between abundant and perfect numbers when I use the...
18369
Roahn Wynar
hahahahastay...
Sep 11, 2006 3:48 am
Sorry about the lame questions, but I am not clear on a point that should be obvious.... My implementation of the Pollard p-1 algorithm seems to work pretty...
18370
Phil Carmody
thefatphil
Sep 11, 2006 6:20 am
... It searches for factors. For an arbitrary prime it will take an excessively long time, as the only factor is the entire number. It's just doing what it ...
18371
Jose Ramón Brox
ambroxius
Sep 17, 2006 9:58 pm
Hi all: Recently, I attended the ICM celebrated in Madrid, and aside from meeting a lot of famous people (like Mandelbrot, Eric Weisstein, Frank Morgan,...
18372
primemind@...
wedsde
Sep 18, 2006 5:58 pm
Hi Prof. Caldwell and members, after 2 mounths of working on a possibly Mersenneprimenumber PFGW unfortunately made an error report : Warning !! Did not valid...
18373
Anton
al_at_i
Sep 20, 2006 7:24 pm
This might surprise: Conjecture: The ratio k_b defined as "the sum of all base-b digits of all the primes between 1 and n" to "n", converges to the constant...
