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42 lines
1.1 KiB
Python
42 lines
1.1 KiB
Python
# Eulers Totient function finds the number of relative primes of a number n from 1 to n
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def totient(n: int) -> list:
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"""
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>>> n = 10
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>>> totient_calculation = totient(n)
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>>> for i in range(1, n):
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... print(f"{i} has {totient_calculation[i]} relative primes.")
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1 has 0 relative primes.
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2 has 1 relative primes.
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3 has 2 relative primes.
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4 has 2 relative primes.
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5 has 4 relative primes.
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6 has 2 relative primes.
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7 has 6 relative primes.
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8 has 4 relative primes.
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9 has 6 relative primes.
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"""
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is_prime = [True for i in range(n + 1)]
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totients = [i - 1 for i in range(n + 1)]
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primes = []
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for i in range(2, n + 1):
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if is_prime[i]:
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primes.append(i)
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for j in range(len(primes)):
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if i * primes[j] >= n:
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break
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is_prime[i * primes[j]] = False
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if i % primes[j] == 0:
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totients[i * primes[j]] = totients[i] * primes[j]
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break
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totients[i * primes[j]] = totients[i] * (primes[j] - 1)
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return totients
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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