euler_p29.py

# Euler - problem 29
"""
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
    22=4, 23=8, 24=16, 25=32
    32=9, 33=27, 34=81, 35=243
    42=16, 43=64, 44=256, 45=1024
    52=25, 53=125, 54=625, 55=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?
"""

# from math import floor
#
# amax, bmax = 100, 100
# bmin = {}
# for a in range(2, bmax): bmin[a] = 1
# count = 0
#
# for a in range(2, 11):
#     count += 100 - bmin[a]
#     for b in range(2, bmax + 1):
#         if a**b in range(2, amax + 1): bmin[a**b] = floor(bmax/b)
# for a in range(11, amax + 1):
#     count += 100 - bmin[a]

numlist = []
for a in range(2, 101):
    for b in range(2, 101):
        if a**b not in numlist: numlist.append(a**b)

print(len(numlist))