# nayuki/Project-Euler-solutions

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 # # Solution to Project Euler problem 95 # Copyright (c) Project Nayuki. All rights reserved. # # https://www.nayuki.io/page/project-euler-solutions # https://github.com/nayuki/Project-Euler-solutions # import itertools def compute(): LIMIT = 10**6 # divisorsum[n] is the sum of all the proper divisors of n divisorsum = [0] * (LIMIT + 1) for i in range(1, LIMIT + 1): for j in range(i * 2, LIMIT + 1, i): divisorsum[j] += i # Analyze the amicable chain length for each number in ascending order maxchainlen = 0 ans = -1 for i in range(LIMIT + 1): visited = set() cur = i for count in itertools.count(1): # 'count' is the length of the this amicable chain visited.add(cur) next = divisorsum[cur] if next == i: if count > maxchainlen: ans = i maxchainlen = count break # Exceeds limit or not a chain (a rho shape instead) elif next > LIMIT or next in visited: break else: cur = next return str(ans) if __name__ == "__main__": print(compute())