Q5.
[3]
Let s be the function that associates with each natural number to the sum of its distinct natural number
divisors.
i.
Calculate s(k) for each natural number k from 1 through 15.
Does there exist a natural number n such that s(n) = 5? Justify your conclusion.
Is it possible to find two different natural numbers m and n such that s(m) = s(n)? Explain.
Use your responses in (ii) and (iii) to determine whether the below statement is true or false.
For each natural number m, there exists a natural number n such that s(n)
iv.
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