Let s be the function that associates with each natural number the sum of its distinct natural number factors. For example,
s(6) = 1 + 2 + 3 + 6
= 12.
1. Calculate s(k) for each natural number k from 1 through 15.
2. Are the numbers SQRT(5), PI, and -6 in the domain of the function s?
What is the domain of the function s?
3. Does there exist a natural number n such that s(n) = 5? Justify your conclusion.
4. Is it possible to find two different natural numbers m and n such that s(m) = s(n)? Explain.
5. Are the following statements true or false? Justify your claim.
1. For each m belonging to Natural numbers, there exists a natural number n such that s(n) = m.
2. For all m and n belonging to natural numbers, if m != n, then s(m) != s(n).