data/problems/29.yml
---
:id: 29
:name: Distinct powers
:url: https://projecteuler.net/problem=29
:content: "Consider all integer combinations of _a_<sup><i>b</i></sup> for 2 ≤ _a_
≤ 5 and 2 ≤ _b_ ≤ 5:\n\n> 2<sup>2</sup>=4, 2<sup>3</sup>=8, 2<sup>4</sup>=16, 2<sup>5</sup>=32
\ \n> 3<sup>2</sup>=9, 3<sup>3</sup>=27, 3<sup>4</sup>=81, 3<sup>5</sup>=243 \n>
4<sup>2</sup>=16, 4<sup>3</sup>=64, 4<sup>4</sup>=256, 4<sup>5</sup>=1024 \n> 5<sup>2</sup>=25,
5<sup>3</sup>=125, 5<sup>4</sup>=625, 5<sup>5</sup>=3125\n\nIf they are then placed
in numerical order, with any repeats removed, we get the following sequence of 15
distinct terms:\n\n4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125\n\nHow
many distinct terms are in the sequence generated by _a_<sup><i>b</i></sup> for
2 ≤ _a_ ≤ 100 and 2 ≤ _b_ ≤ 100?\n\n"