To me, 256 is really the perfect number. It is 2^8 (or 2^2^2^2).

Nah, 49's not perfect, it's just cooler than 50. Perfect numbers are actually a defined mathematical concept, and 1 is included. Take those as unrelated statements.

59) People don't get and then overanalyze math jokes.

Also, 256 is 2^2^3, not 2^2^2^2. 2^2^2^2 is 65536. (2^2)^(2^2) is 256.

OK, so I did a little research (and in the end overanalyzed it further). 496 is a perfect number, but your explanation was *seriosuly* lacking.

http://en.wikipedia.org/wiki/496_(number)

Specifically, your sum of the divisiors is not even close to accurate. The part of the perfection involving that is actually:

"496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case."

And 2^2^3 is not 256. 2^(2^3) is but then you are reversing the order of your powers. Powers work left to right. 2 squared =4 which squared =16 which squared =256. so while 2^8 is 256 and 8 is 2^3, 2^2^3 =/= 2(2^3). In fact, it would equal (2^2)^3 which happens to be 64.

left out a mathematical symbol... @^2^3 =/= 2^(2^3)

Damn it! you get what I mean...

Hey, you've lost us. Maybe that was the intention.

#lolwut

From http://en.wikipedia.org/wiki/Perfect_number
"In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum)."
What the hell have you been smoking?

Anyway, in my experience, "^" as an exponentiation operator doesn't work like other mathematical operations. It usually raises to everything following it until it meets a "lower" operation, assuming parentheticals have been simplified. Go check with Google, Wolfram, or any number of other programming languages.

This is why everything needs to be done in reverse polish.

Ah, I found the source of your confusion. You missed "Also related to its being a perfect number," at the beginning of your wiki quote.

I could jist try a simple program in C# and see what it does.

And you missed the oversimplification of the divisors aka factors in your reason. The equation you gave had absolutelt nothing to do with it and, in fact, is incorrect. It involves a division that results in a whole number which you overlooked.

But then we are now providing point 314.159

I just did so with Python, Google, and Mathematica.

It's number theory, what the hell else does divisor mean?

They are properly called factors. They are only the divisor when put into an equation with division in it. For example, 49/43 is an equation with 43 as the divisor, but it is not a factor of 49.

And Microsoft must have an error in their math engine if Python, Google, and Mathematica all say 2^2^2^2 is 65K because Excel says 2^2^2^2 = 256.

And interestingly enough, Google's calculator was forced to put the parenthesis to do it in reverse order, so I wouldn't trust it to know what it is doing.

Excel has some weird problems with operation precedence. I would trust Mathematica for anything math related. Speaking of which, http://mathworld.wolfram.com/Divisor.html

http://en.wikipedia.org/wiki/Operator_associativity#A_detailed_example

Bejeezus! "Reasons Not to Use the Forum"

I have to take your word on Mathematica. I'm not a student and $300 is a lot to spend when I can code the equations I use in C#.

What is interesting is that my old copy of the Handbook of Applied Mathematics says a divisor is any number taken into the dividend and that a factor is a proper divisor, that is a divisor that is a whole number and whose matching divisor is also a whole number and that the factors include a subset of prime factors which are the prime numbered factors and are also often called prime divisors. this decision to limit divisors and equate them with factors must be a new aspect of mathematics (within the last 25 years).

I mean Mathworld and WolframAlpha, I'm not going to spend that much money on software, even software as nice as Mathematica.

I think it's just the pure mathematicians not communicating with the applied mathematicians. Number theoretical definitions are often different than applied ones.

And so a little research shows that VB has it worong (all math operators are left associative when they have equa precedence) and C# gets around it by not even having a exponetial operator and instead using the Math.Pow function (I forgot about that), forcing one to chose the order because it only takes two parameters...

I learned something new today. It was a good day after all.

Well, I work in the applied mathematics world, not the theoretical one, so the HoAM and the HoCP are my bibles when coding various mathematical formula (especially iterative ones like Gaussian equations for worst case event analysis) for my customers.

I'm pretty sure exponentiation is right associative, but in the grand scheme of things it doesn't matter. I fully understand the confusion on the divisor thing. When doing anything computer scientific, I would probably say factor, but when I'm talking number theory, I spout number theory.

Yeah, everything I see except for VB indicates other programmig languages with the operator are right-associative. So it's properly (((2^2)^2)^2) = 256 and 2^2^2^2=65536. Like I said, I learned something today so that sort of makes up for spending the whole morning in the hospital with the wife.

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