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Square root smooth Numbers

Published on Saturday, 4th May 2019, 07:00 pm; Solved by 319

Problem 668

A positive integer is called square root smooth if all of its prime factors are strictly less than its square root.
Including the number $1$, there are $29$ square root smooth numbers not exceeding $100$.

How many square root smooth numbers are there not exceeding $10\,000\,000\,000$?