## Overview

### Question

Consider all integer combinations of $$a^b$$ for $$2 \leq a \leq 5$$ and $$2 \leq b \leq 5$$: \begin{aligned} & 2^2 = 4\text{, } 2^3 = 8\text{, } 2^4 = 16\text{, } 2^5 = 32 \\ & 3^2 = 9\text{, } 3^3 = 27\text{, } 3^4 = 81\text{, } 3^5 = 243 \\ & 4^2 = 16\text{, } 4^3 = 64\text{, } 4^4 = 256\text{, } 4^5 = 1024 \\ & 5^2 = 25\text{, } 5^3 = 125\text{, } 5^4 = 625\text{, } 5^5 = 3125 \end{aligned} If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms: $$4\text{, } 8\text{, } 9\text{, } 16\text{, } 25\text{, } 27\text{, } 32\text{, } 64\text{, } 81\text{, } 125\text{, } 243\text{, } 256\text{, } 625\text{, } 1024\text{, } 3125$$ How many distinct terms are in the sequence generated by $$a^b$$ for $$2 \leq a \leq 100$$ and $$2 \leq b \leq 100$$?

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9183