- #1

phymath7

- 48

- 4

- Homework Statement
- The sum of divisor function σ(n) returns the sum of all positive divisors d of the number n. We denote ##N_k## any number that fulfils the following condition:

σ(##N_K##) ≥##k.N_K##.

Find examples for ##N_3##;##N_4##;##N_5## and prove that they fulfil this condition.

- Relevant Equations
- ##σ(n)=\frac{p_{1}^{a_1+1}-1}{p_1-1}.\frac{p_{2}^{a_2+1}-1}{p_2-1}.......\frac{p_{k}^{a_k+1}-1}{p_k-1}##

I've found that ##N_1## is 1. But it's really tiresome to find them one by one. I also tried to use the equation but couldn't. Please help me out.