2023 IOQM/Problem 9

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Problem

Find the number of triples $(a, b, c)$ of positive integers such that (a) $ab$ is a prime; (b) $bc$ is a product of two primes; (c) $abc$ is not divisible by square of any prime and (d) $abc ≤ 30$ (Error compiling LaTeX. Unknown error_msg)