# Arranging Consecutive Integers in a Continued Radical to Make a Rational Number

Find the sum of all positive integral $$n$$ such that there exists a permutation $$\sigma$$ of the set $$\{ 1,\ldots, n\}$$ such that

$\sqrt{\sigma(1)+\sqrt{\sigma(2)+\sqrt{\cdots+\sqrt{\sigma(n)}}}}$

is a rational number. $$\sigma(m)$$ denotes the $$m$$-th term of the permutation.

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