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?

unklerhaukus · Answer

@ParthKohli

parthkohli · Answer

Sounds like a programming question to me.