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The smallest number nn greater than 1 such that n\large \sqrt{n}, n3\large \sqrt[3]{n}, n4\large \sqrt[4]{n}, n5 \large \sqrt[5]{n}, n6 \large \sqrt[6]{n}, n7 \large \sqrt[7]{n}, n8 \large \sqrt[8]{n}, n9 \large \sqrt[9]{n}, n10 \large \sqrt[10]{n} are all integers can be expressed in the form aba^{b}, where aa and bb are both positive integers and with aa as small as possible.

Find a+ba+b.

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