def solve():
factors = [0] * 20
accum = 1
sieve(20)
for i in xrange(1, 21):
for p,k in factor(i):
if k > factors[p-1]:
accum *= p ** (k - factors[p-1])
factors[p-1] = k
return accum
def I(n):
terms = []
for (p,k) in factor(n):
if p % 2 == 0 and k>1:
residues = (1, -1, (1<<k-1)-1, (1<<k-1)+1)
else:
residues = (1, -1)
pk = p**k
coef = n // pk * modInverse(n // pk, pk)
terms.append(map(lambda x: x*coef, residues))
return max(filter(lambda x: x != n-1, (sum(res) % n for res in cross(*terms))))
def factor(n, primes=None):
return set(lib.factor(n, primes=primes).items())
from eulerlib import factor factors = factor(600851475143) print factors[len(factors) - 1]
def divisors(n):
if n == 1: return 1
F = factor(n)
return reduce(lambda x, y: x * y, [F.count(i) + 1 for i in set(F)])
from eulerlib import factor n = 1 while True: satisfied = True for i in xrange(n,n+4): if len(set(factor(i))) != 4: satisfied = False break if satisfied: print range(n,n+4) break n += 1
from eulerlib import factor factors = factor(600851475143) print factors[len(factors)-1]
def divisors(n): if n == 1: return 1 F = factor(n) return reduce( lambda x,y: x*y , [F.count(i)+1 for i in set(F)] )