<|file_name|>pe029_distinct_powers.py<|end_file_name|><｜fim▁begin｜>#!/usr/bin/env python
# coding=utf-8
"""
Distinct powers
Problem 29

Consider all integer combinations of ab 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 ab for 2 ≤ a ≤ 100 and
2 ≤ b ≤ 100?
"""
from __future__ import print_function


def power_combinations(a, b):
    for i in range(2, a):
        for j in range(2, b):
            yield i ** j


if __name__ == '__main__':
    print(len(set(po    <|fim_middle|>
<｜fim▁end｜>
    wer_combinations(101, 101))))  # 9183
