33 lines
951 B
Python
33 lines
951 B
Python
# https://docs.sympy.org/latest/modules/ntheory.html#sympy.ntheory.factor_.divisors
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from sympy import divisors
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def chowla(n):
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return 0 if n < 2 else sum(divisors(n, generator=True)) - 1 -n
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def is_prime(n):
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return chowla(n) == 0
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def primes_to(n):
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return sum(chowla(i) == 0 for i in range(2, n))
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def perfect_between(n, m):
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c = 0
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print(f"\nPerfect numbers between [{n:_}, {m:_})")
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for i in range(n, m):
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if i > 1 and chowla(i) == i - 1:
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print(f" {i:_}")
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c += 1
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print(f"Found {c} Perfect numbers between [{n:_}, {m:_})")
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if __name__ == '__main__':
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for i in range(1, 38):
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print(f"chowla({i:2}) == {chowla(i)}")
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for i in range(2, 6):
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print(f"primes_to({10**i:_}) == {primes_to(10**i):_}")
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perfect_between(1, 1_000_000)
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print()
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for i in range(6, 8):
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print(f"primes_to({10**i:_}) == {primes_to(10**i):_}")
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perfect_between(1_000_000, 35_000_000)
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