2023 SSMO Accuracy Round Problems/Problem 5

Problem

Define the $\textit{relationship}$ between two numbers $a$ and $b$ to be $\frac{\sigma(ab)}{\sigma(a)\sigma(b)}$ where $\sigma(x)$ is the number of divisors of $x$ . Find the sum of integers $1 \le n \le 100$ which have a relationship of $\frac{3}{4}$ with $360$ .

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2023 SSMO Accuracy Round Problems/Problem 5

Problem

Solution