Results 1 to 5 of 5

Math Help - Sigma Function Help

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    11

    Sigma Function Help

    Sigma Function

    σ: ℕ ->ℕ

    n
    Σ k = σ (n)
    k|n

    1. Is the Sigma Fctn an injection?
    2. Is it a surjection?
    3. Can you find a formula for the sigma fctn which allows to calculate the sum of divisors of n based on the decomposition of n into a product of prime numbers?

    Thanks guys!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by suissa View Post
    n
    Σ k = σ (n)
    k|n

    1. Is the Sigma Fctn an injection?
    2. Is it a surjection?
    3. Can you find a formula for the sigma fctn which allows to calculate the sum of divisors of n based on the decomposition of n into a product of prime numbers?
    1) Consider n=15,23.
    2) Can it be that \sigma (n) = 2?
    3) If n=p_1^{a_1}...p_n^{a_n} then \sigma (n) = \frac{p_1^{a_1}-1}{p_1-1}\cdot ... \cdot \frac{p_n^{a_n}-1}{p_n-1}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Dec 2007
    From
    Melbourne
    Posts
    428
    Sorry please ignore this, the perfect hacker already answered in more detail and clarity

    1. Is the Sigma Fctn an injection?
    No. Look for a counter-example, it shouldn't take too long.

    2. Is it a surjection?
    No. look for another counter-example

    3. Can you find a formula for the sigma fctn which allows to calculate the sum of divisors of n based on the decomposition of n into a product of prime numbers?
    Yes.
    If n = \prod_{i=0}^ma_i^{k_i} where all a are prime,
    then \sigma(n) = \prod_{i=0}^m\sum_{j_i=0}^{k_i}a_i^{j_i}
    This can be simplified using the formula for geometric series
    Last edited by badgerigar; December 6th 2007 at 08:19 PM. Reason: Perfect hacker beat me to it
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2007
    Posts
    11
    I'm sorry I don't understand 1 and 2.
    Thanks a lot for the reply though!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2007
    Posts
    11
    Oh I understand it.
    Thanks PerfectHacker and badgerigar
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Choosing a sigma algebra such that a function is measurable
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 3rd 2011, 12:52 PM
  2. Show intersection of sigma-algebras is again a sigma-algebra
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 20th 2010, 07:21 AM
  3. how to determine sigma and sgn(sigma) for matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 16th 2010, 11:12 AM
  4. sigma function help
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: July 18th 2008, 11:55 PM
  5. Sigma function help
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 21st 2008, 04:58 PM

Search Tags


/mathhelpforum @mathhelpforum