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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 \(\frac{\phi (n) \cdot \sigma (n)}{n^{2}}\)