MATH 319 Problem Set The Last

1. Find the smallest positive integer n such that d(n) = 10.

2. Find the smallest positive integer n such that d(n) = 12.

3. Prove that n is a square if and only if d(n) is odd.

4. Let . Compute F(20).

5. Recall the definition of Show that . (Hint: Since both functions, and d, are multiplicative one can compute F(n) by computing F for prime powers.)

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