problem-029.py

### Problem 29 - Distinct Powers
###--------------------------------------------------------------------------------------------------------------------------
### 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 a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

### Solution

terms = []

for a in range(2, 101):
    for b in range(2, 101):
        value = a ** b
        if value not in terms:
            terms.append(value)

print("The number of distinct terms is: " + str(len(terms)))