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 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_11}.\frac{p_{2}^{a_2+1}1}{p_21}.......\frac{p_{k}^{a_k+1}1}{p_k1}##
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.