# Infinite Sum from Radicals

**Number Theory**Level 4

Let \(\text{rad}(n)\) be the product of distinct prime factors of \(n\). (For example, \(\text{rad}(20)=2\cdot 5=10\) since \(20=2^2\cdot 5\)). Consider the set \[\begin{aligned} S=\{n\in\mathbb{N}\mid \text{rad}(n)=30\} \end{aligned}\] and let \(T=\displaystyle\sum_{n\in S}\dfrac{1}{n^2}\). Find the value of \(\dfrac{1}{T}\).