1.44 The increasing sequence $2,3,5,6,7,10,11, \cdots$, contains all positive integers that are neither perfect squares nor perfect cubes. Find the 500th term of this sequence.
[Solution] It is easy to know that $[\sqrt{500}]=22, [\sqrt[3]{500}]=7, [\sqrt[6]{500}]=2, ([x]$ represents the largest integer not exceeding $x$).
Therefore, there are $22+7-2=27$ square numbers or cube numbers within the natural number 500. Now consider how many square numbers or cube numbers there are from $501 \sim 530$, by calculation, there is only one number $512=8^{3}$. Therefore,
$$
a_{500}=500+27+1=528 .
$$