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For each integer n ge 1, define a (n) = ...

For each integer `n ge 1,` define `a _(n) = [ (n)/( [sqrtn]) ],` where [x] denotes the largest integer not exceeding x, for any real number x. Find the number of all n is the set `{1,2,3,….,2010}` for which `a _(n)gt a _(n+1).`

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The correct Answer is:
`2 ^(2)-1, 3 ^(2)-1,…..,44^(2)-1`
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