57 lines
1.3 KiB
Python
57 lines
1.3 KiB
Python
import math
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def is_prime(n):
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if n == 2 or n == 3: return True
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if n < 2 or n%2 == 0: return False
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if n < 9: return True
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if n%3 == 0: return False
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r = int(n**0.5)
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f = 5
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while f <= r:
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if n%f == 0: return False
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if n%(f+2) == 0: return False
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f +=6
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return True
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def tot(n):
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if is_prime(n):
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return n-1
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else:
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return len([i for i in range(1,n) if math.gcd(i,n)==1])
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def phi(n) :
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result = n # Initialize result as n
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# Consider all prime factors
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# of n and for every prime
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# factor p, multiply result with (1 - 1 / p)
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p = 2
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while(p * p<= n) :
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# Check if p is a prime factor.
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if (n % p == 0) :
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# If yes, then update n and result
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while (n % p == 0) :
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n = n // p
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result = result * (1.0 - (1.0 / (float) (p)))
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p = p + 1
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# If n has a prime factor
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# greater than sqrt(n)
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# (There can be at-most one
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# such prime factor)
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if (n > 1) :
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result = result * (1.0 - (1.0 / (float)(n)))
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return (int)(result)
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max = [0,0]
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for n in range(2,1000001):
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totn = phi(n)
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if n/totn > max[1]:
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max = [n, n/totn]
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print(max) |