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anonymous
 one year ago
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?
anonymous
 one year ago
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?

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