Consider all integer combinations of \(a^b\) for \(2 ≤ a ≤ 5\) and \(2 ≤ b ≤ 5\):
\[2^2=4, 2^3=8, 2^4=16, 2^5=32\] \[3^2=9, 3^3=27, 3^4=81, 3^5=243\] \[4^2=16, 4^3=64, 4^4=256, 4^5=1024\] \[5^2=25, 5^3=125, 5^4=625, 5^5=3125\]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 \(2 ≤ a ≤ 100\) and \(2 ≤ b ≤ 100\)?