How to generate number in ascending order using the expression $a^2\cdot b^3$ where $a$ and $b$ are distinct primes. How to generate numbers in ascending order using the expression $a^2\cdot b^3$ where $a$ and $b$ are distinct primes.
Here are a couple of examples :
$$\begin{array}{c|ccc}
\text{No}&a&b&a^2\cdot b^3\\
\hline
1&3&2&72\\
2&2&3&108\\
3&5&2&200\\
4&7&2&392\\
5&2&5&500\\
6&5&3&675\\
7&11&2&968\\
8&3&5&1125\\
9&7&3&1323\\
10&13&2&1352\\
\end{array}$$
Is there a way I can stop at $1000$th number without pre computing say $100000$ numbers, and then sorting and arriving at $1000$th number ?

I got Matlab to calculate numbers up to $10^8$, or a hundred billion.
The $N$th number, over that range, was about $9N^{2.5}/\ln N$.  The $1000$th number was $42797187 = 3^31259^2$.
The largest prime involved in the first thousand was $2311$, which is the $344$th prime.
According to my formula, the biggest prime $p$, which will be with $2^3p^2\approx 9N^{2.5}/\ln N$, is roughly $p=N^{1.25}/\sqrt{\ln N}$.
