Project Euler Problem 29

问题：

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:

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?

答案：9183

      duplication

4 --> 49
8 --> 49
9 --> 49
16 --> 58
25 --> 49
27 --> 49
32 --> 48
36 --> 49
49 --> 49
64 --> 62
81 --> 58
100 --> 49 sum = 618

99  50   50   41   51   37
2   4    8    16   32   64 //Use the set data structure, count the number of 2's exponent.
3   9    27   81
5   25
6   36
7   49
10  100

result = 99*99-618 = 9183