1. 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
3^7=9, 3^3=27, 3^4=81, 3^5=243
4^3=16, 4^3=64, 4^4=256, 4^3=1024
5^7=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 for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?