100 lines
2.2 KiB
Python
100 lines
2.2 KiB
Python
from functools import reduce
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from tools import number_theory
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from tools import algebra
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import sys
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def next_lst(lst, std):
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for i in range(len(lst)):
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if lst[i] < std[i]:
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lst[i] += 1
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lst[:i] = [0] * i
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return True
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else:
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return False
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def implode(p_lst, e_lst):
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return reduce(lambda x, y: x * (y[0] ** y[1]), zip(p_lst, e_lst), 1)
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def factor(k):
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p = 2
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p_lst = []
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e_lst = []
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while p ** 2 <= k:
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if not k % p:
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e = 0
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while not k % p:
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e += 1
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k //= p
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p_lst.append(p)
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e_lst.append(e)
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p += 1
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if k > 1:
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p_lst.append(k)
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e_lst.append(1)
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return p_lst, e_lst
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def pow_factor(k):
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p_lst, e_lst = factor(k)
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e_lst = list(map(lambda x: x * 2, e_lst))
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g_lst = [0] * len(e_lst)
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result = [1]
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while next_lst(g_lst, e_lst):
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result.append(implode(p_lst, g_lst))
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return list(sorted(result))
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def simplify(x, y):
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d = number_theory.gcd(x, y)
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return x // d, y // d
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def try_root(rest, a, b):
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if rest < a:
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return 0
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q, r = divmod(rest - a, b)
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if r:
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return 0
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u = algebra.is_root(q, 3)
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if u != a:
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return u
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return 0
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def calc_k(k):
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n = k ** 2
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pf = pow_factor(k)
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lf = len(pf)
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for i in range(lf):
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t = pf[i]
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for j in range(i, lf - i):
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v = pf[j]
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rest = n // t // v
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if rest > 0:
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if try_root(rest, t, v):
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return n
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if try_root(rest, v, t):
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return n
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def search(limit):
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for k in range(1, int(limit ** 0.5) + 1):
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n = calc_k(k)
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if n:
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yield n
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def debug(limit):
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total = 0
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k = 1
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n = 1
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while n < limit:
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for r in range(1, n):
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U, V = simplify(n - r, r ** 2)
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u = algebra.is_root(U, 3)
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v = algebra.is_root(V, 3)
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if u * v:
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total += n
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print(k, n, r, r*U//V, r*U*U//V//V)
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k += 1
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n = k ** 2
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print(total)
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#print(calc_k(int(sys.argv[1])))
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#print(sum(search(int(sys.argv[1]))))
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debug(100000)
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