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Minimal sigma-totient product

Description

For a positive integer $$n$$, let $$\phi (n)$$ be the number of integers less than $$n$$ that are relatively prime to $$n$$.  For example, $$\phi (9) = 6$$, counting 1, 2, 4, 5, 7, and 8.

Additionally, let $$\sigma (n)$$ be the sum of all divisors of $$n$$.  For example, $$\sigma (16) = 1+2+4+8+16 = 31$$.

Question

Over the integers $$1\leq n \leq 10000$$, find the value of $$n$$ that minimizes $$\frac{\phi (n) \cdot \sigma (n)}{n^{2}}$$

Over the integers $$1\leq n \leq 10000$$, find the value of $$n$$ that minimizes $$\frac{\phi (n) \cdot \sigma (n)}{n^{2}}$$