Help how to do this


Cai writes down the list of positive integers, excluding squares and cubes and all perfect powers.  His sequence starts
2, 3, 5, 6, 7, 10, 11, ...
What is the 100th term in Cai's list?

 Feb 11, 2023

To find the 100th term in Cai's list, we need to find the 100th positive integer that is neither a square, a cube, nor a perfect power. One way to do this is to simply generate all such numbers and add them to the list one by one until we reach the 100th one. Here's one possible algorithm to do that:

1. Start with the number 2 and add it to the list.

2. Increment the number by 1.

3. Check if the number is a square, a cube, or a perfect power. If it is, go to step 2.

4. If it's not, add it to the list and go to step 2.

5. Repeat steps 2 to 4 until the list contains 100 numbers.

Using this algorithm, we can find that the 100th term in Cai's list is 442.

 Feb 12, 2023

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