Consider all integer combinations of ab 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 $2 ≤ b ≤ 100$?
s = len(set([a**b for a in range(2, 101) for b in range(2, 101)]))
assert(s == 9183)
print(s)