1. ## Sigma Function

Hi, I stumbled upon a question in my homework that mentioned sigma functions, and as I under stood, a sigma function is the sum of the factors of a number. Ex. f(5)= 5+1 (factors) = 6.

I would like to know why this is so, Sigma function, does it have any other purpose ? And I thought functions are represented by equations? I hope my questions are clear because I feel like they are not >.<!

-Cheers!

2. ## Re: Sigma Function

Originally Posted by sakonpure6
Hi, I stumbled upon a question in my homework that mentioned sigma functions, and as I under stood, a sigma function is the sum of the factors of a number. Ex. f(5)= 5+1 (factors) = 6.

I would like to know why this is so, Sigma function, does it have any other purpose ? And I thought functions are represented by equations?
Usually $\displaystyle \sigma(5)=2$ is the number of factors of five.
A "function" is any rule that to a specific "object" (typically a number but not necessarily), x, in a given set of objects, assigns a unique object, y. A different way of saying the same thing is "a set of ordered pairs of objects such that two different pairs cannot have the same first member. A function is NOT necessarily given by a formula. For example, the function defined by the formula $\displaystyle y= x^2$, with x any real number, is the set of ordered pairs, $\displaystyle \{(x, x^2)| x\in R\}$. Notice that the statement of the domain is an important part of the definition of the function. The set of ordered pairs, $\displaystyle \{(x, x^2)| x\in R, x\ge 0\}$, while having the same "formula" is a completely different function.