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alex41 [277]
3 years ago
12

The sequence 2, 3, 5, 6, 7, 10, 11, $\ldots$ contains all the positive integers from least to greatest that are neither squares

nor cubes. what is the $400^{\mathrm{th}}$ term of the sequence?
Mathematics
1 answer:
sergeinik [125]3 years ago
7 0
The 400th term is 425.

There are floor(√400) = 20 squares in the range 1..400, so the 400th term will be at least 420. There are floor(∛420) = 7 cubes in the range 1..400, so the 400th term may be as high as 427. However, there are \lfloor\sqrt[6]{427}\rfloor=2 numbers that are both squares and cubes. Consequently, the 400th term will be 427-2 = 425.
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