Statement

Consider all integer combinations of $a^b$ for $2 \le a \le 5$ and $2 \le b \le 5$:

$2^2 = 4,\ 2^3 = 8,\ 2^4 = 16,\ 2^5 = 32$
$3^2 = 9,\ 3^3 = 27,\ 3^4 = 81,\ 3^5 = 243$
$4^2 = 16,\ 4^3 = 64,\ 4^4 = 256,\ 4^5 = 1024$
$5^2 = 25,\ 5^3 = 125,\ 5^4 = 625,\ 5^5 = 3125$

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by $a^b$ for $2 \le a \le 100$ and $2 \le b \le 100$?

Solution

Simple brute-force solution using Python's structures.

if __name__ == '__main__':
    result = set()
    for a in range(2,100+1):
        for b in range(2, 100+1):
            num = a ** b
            result.add(num)
    print("The result is:", len(result))

The Python file is available for download here.