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!
Sorry please ignore this, the perfect hacker already answered in more detail and clarity
No. Look for a counter-example, it shouldn't take too long.1. Is the Sigma Fctn an injection?
No. look for another counter-example2. Is it a surjection?
Yes.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?
If n = where all a are prime,
then
This can be simplified using the formula for geometric series