Python/project_euler/problem_29/sol1.py

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"""
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?
"""
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def solution(n: int = 100) -> int:
"""Returns the number of distinct terms in the sequence generated by a^b
for 2 <= a <= 100 and 2 <= b <= 100.
>>> solution(100)
9183
>>> solution(50)
2184
>>> solution(20)
324
>>> solution(5)
15
>>> solution(2)
1
>>> solution(1)
0
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"""
collectPowers = set()
currentPow = 0
N = n + 1 # maximum limit
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for a in range(2, N):
for b in range(2, N):
currentPow = a ** b # calculates the current power
collectPowers.add(currentPow) # adds the result to the set
return len(collectPowers)
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if __name__ == "__main__":
print("Number of terms ", solution(int(str(input()).strip())))