euler_029.py

# Euler 29
# 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 ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

powers = set()
UPPER_BOUND = 100

for a in range(2,UPPER_BOUND+1):
    for b in range(2,UPPER_BOUND+1):
        p = a**b
        powers.add(p)

print(len(powers))