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 \(a^b\) 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 \(a^b\)：
\[2^2=4, 2^3=8, 2^4=16, 2^5=32\] \[3^2=9, 3^3=27, 3^4=81, 3^5=243\] \[4^2=16, 4^3=64, 4^4=256, 4^5=1024\] \[5^2=25, 5^3=125, 5^4=625, 5^5=3125\]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：
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
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？
result = []
for a in range(2, 101):
for b in range(2, 101):
power = 1
for i in range(0, b):
power = power * a
if not power in result:
result.append(power)
print len(result)
感想：
- 暴力破解什么时候可以停止
- python的range的范围有点晕