Question

What is the third perfect number? Please help me understand how it works. thnx

Answer 1

1^2 = 1
2^2 = 4
3^2 = 9

The third perfect number is 9? Did you mean perfect SQUARES?

Answer 2

ohh, no, ummm, like the first number is 6, the second is 28, and idk what the third is...plus idk how to get the number

Answer 3

Aperfect number is a positive integer that is equal to the sum of its proper positive divisors.

Mathematically, \( \sigma_1(N)=2N \)

\(\sigma_1() \) is the divisor function ( http://en.wikipedia.org/wiki/Divisor_function)

Here is the list of perfect numbers in OEIS: http://oeis.org/A000396

Answer 4

Never heard of it

Answer 5

And fool clearly wiki'd it

Answer 6

A year back I wrote a very optimized perfect number generator.

Answer 7

whoa, did you code it all?

Answer 8

Unfortunately it's a part of an algorithm contest, so I can't share the code here. But I can give some hints if you want :)

Answer 9

Hero, I don't really need to wike perfect numbers :)

Answer 10

Yes please, any that are available :) I just started coding a few days ago and I'm working through the Python textbook. Just started my first more complex code (finding slope and y-intercept)still very simple, but I'd appreciate it

Answer 11

Okay first there are no odd perfect numbers (this is not proven yet) so you can clearly ignore the odd numbers.

Answer 12

ok

Answer 13

Why am I just now hearing about perfect numbers? In what course do you usually learn about them?

Answer 14

14yamaka, what course are you currently taking?

Answer 15

Now, you need to have a very fast \( \sigma_1(N) \) for that you need to have a fast optimized prime generator. This is actually deep I have used Miller Rabin algorithm.

Answer 16

@Hero: Elementary Number theory.

Answer 17

14yamaka, I would probably advice you to be satisfied with typical brute-force at this stage :)

Answer 18

*This is actually deep, I have used Miller Rabin algorithm + sieve.

Answer 19

wow, ok, I gotta read up on this Miller Rabin algorithm. and sieve. Thanks for the explanation. Both of you :)

Answer 20

Fain I help :)

Answer 21

I didn't provide anything, lol

FFM provided everything