Problem 668

Square root smooth Numbers

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 $10 000 000 000$ ?

平方根光滑数

若一个正整数的所有质因数都严格小于它的平方根，则称之为平方根光滑数。
包括 $1$ 在内，有 $29$ 个不超过 $100$ 的平方根光滑数。.

有多少个不超过 $10 000 000 000$ 的平方根光滑数？