Problem 29

Problem 29

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

仔细看看以下a与b的组合

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:

如果移除重复项，并排序，得出如下：

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

有多少个不重复的数字可以由a的b次方得出？(2 ≤ a ≤ 100 and 2 ≤ b ≤ 100)

How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

import math
sequence = []
for a in range(2, 101):
    for b in range(2, 101):
        sequence.append(math.pow(a, b))
print(len(set(sequence)))  # 将列表转换为集合，自动去重