Let 2,3,5,6,7,10,11,... be an increasing sequence of positive integers that are neither the perfect squares nor the cubes. Find the 1991st term.

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- Jan 13th 2011, 07:37 PMchris86find the 1991st term
Let 2,3,5,6,7,10,11,... be an increasing sequence of positive integers that are neither the perfect squares nor the cubes. Find the 1991st term.

- Jan 13th 2011, 07:57 PMchiph588@
Let's define to be the number of numbers less than or equal to such that they are neither the perfect squares or cubes.

We then have .

The intuition behind is we take every number up to and then subtract all of the perfect squares and cubes. We must then account for any duplicates.

Now solve . - Jan 13th 2011, 08:05 PMchiph588@