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Distinct Natural Number Function

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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).

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Solution Summary

This solution provides an illustration of distinct natural numbers and an associated function.

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** Please see the attached file for the complete solution response **

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. 1. Calculate s(k) for each natural number k from 1 through 15.
2.
(please see the attached file)

3. 2. Are the numbers (please see the attached file), (please see the attached file), and -6 in the domain of the function s?
4. What is the domain of the function s?
No, the function ...

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