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Let's try counting the number of perfect squares and cubes less than . There are twenty perfect squares less than 441: . There are also seven perfect cubes less than 441: . So there would seem to be 20+7=27 numbers less than 441 which are either perfect squares and perfect cubes.
But wait! is both a perfect square and a perfect cube, so we've accidentally counted it twice. Similarly, we've counted any sixth power less than 441 twice because any sixth power is both a square and a cube at the same time. Fortunately, the only other such one is . Thus, there are 27-2=25 numbers less than 441 that are perfect squares or perfect cubes. Also, since and , then all 25 of these numbers are no more than 400. To compensate for these twenty-five numbers missing from the list, we need to add the next twenty-five numbers: 401, 402, , 424, 425, none of which are perfect square or perfect cubes. Thus, the term is .