problem 29 // project euler

Distinct powers

Consider all integer combinations of a^b 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:

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

不同的幂

考虑所有满足2 ≤ a ≤ 5和2 ≤ b ≤ 5的整数组合生成的幂a^b：

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

如果把这些幂按照大小排列并去重，我们得到以下由15个不同的项组成的序列：

在所有满足2 ≤ a ≤ 100和2 ≤ b ≤ 100的整数组合生成的幂a^b排列并去重所得到的序列中，有多少个不同的项？