A positive integer is called a perfect power if it can be written in the form $a^b,$ where $a$ and $b$ are positive integers with $b \geq 2.$ For example, $32$ and $125$ are perfect powers because $32 = 2^5$ and $125 = 5^3.$

The increasing sequence $$ 2, 3, 5, 6, 7, 10, \ldots $$ consists of all positive integers which are not perfect powers. What is the sum of the squares of the digits of the $$1000^\text{th}$$ number in this sequence?

Question

A positive integer is called a perfect power if it can be written in the form $a^b,$ where $a$ and $b$ are positive integers with $b \geq 2.$ For example, $32$ and $125$ are perfect powers because $32 = 2^5$ and $125 = 5^3.$

The increasing sequence $$ 2, 3, 5, 6, 7, 10, \ldots $$ consists of all positive integers which are not perfect powers. What is the sum of the squares of the digits of the $$1000^\text{th}$$ number in this sequence?