def radical(n):
"""Calculates the radical, the product of the unique prime factors of the given integer"""
return reduce(op.mul, get_prime_factors(n).keys(), 1)
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""
from euler import op, reduce
n = "73167176531330624919225119674426574742355349194934"+ \
"96983520312774506326239578318016984801869478851843"+ \
"85861560789112949495459501737958331952853208805511"+ \
"12540698747158523863050715693290963295227443043557"+ \
"66896648950445244523161731856403098711121722383113"+ \
"62229893423380308135336276614282806444486645238749"+ \
"30358907296290491560440772390713810515859307960866"+ \
"70172427121883998797908792274921901699720888093776"+ \
"65727333001053367881220235421809751254540594752243"+ \
"52584907711670556013604839586446706324415722155397"+ \
"53697817977846174064955149290862569321978468622482"+ \
"83972241375657056057490261407972968652414535100474"+ \
"82166370484403199890008895243450658541227588666881"+ \
"16427171479924442928230863465674813919123162824586"+ \
"17866458359124566529476545682848912883142607690042"+ \
"24219022671055626321111109370544217506941658960408"+ \
"07198403850962455444362981230987879927244284909188"+ \
"84580156166097919133875499200524063689912560717606"+ \
"05886116467109405077541002256983155200055935729725"+ \
"71636269561882670428252483600823257530420752963450"
print(max(reduce(op.mul, map(int, n[i : i + 5]), 1) for i in range(len(n) - 5)))
#!/usr/bin/env python
"""
Problem 005:
2520 is the smallest number that can be divided by each of the numbers from 1 to
10 without any remainder.
What is the smallest number that is evenly divisible by all of the numbers from
1 to 20?
"""
from euler import get_prime_factors, op, reduce
N = 20
factors = {}
for n in range(1, N + 1):
for k, v in get_prime_factors(n).items():
if k in factors:
if v > factors[k]:
factors[k] = v
else:
factors[k] = v
print(reduce(op.mul, [k**v for k, v in factors.items()], 1))
def radical(n):
"""Calculates the radical, the product of the unique prime factors of the given integer"""
return reduce(op.mul, get_prime_factors(n).keys(), 1)
#!/usr/bin/env python
"""
Problem 005:
2520 is the smallest number that can be divided by each of the numbers from 1 to
10 without any remainder.
What is the smallest number that is evenly divisible by all of the numbers from
1 to 20?
"""
from euler import get_prime_factors, op, reduce
N = 20
factors = {}
for n in range(1, N + 1):
for k, v in get_prime_factors(n).items():
if k in factors:
if v > factors[k]:
factors[k] = v
else:
factors[k] = v
print(reduce(op.mul, [k**v for k, v in factors.items()], 1))
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""
from euler import op, reduce
n = "73167176531330624919225119674426574742355349194934"+ \
"96983520312774506326239578318016984801869478851843"+ \
"85861560789112949495459501737958331952853208805511"+ \
"12540698747158523863050715693290963295227443043557"+ \
"66896648950445244523161731856403098711121722383113"+ \
"62229893423380308135336276614282806444486645238749"+ \
"30358907296290491560440772390713810515859307960866"+ \
"70172427121883998797908792274921901699720888093776"+ \
"65727333001053367881220235421809751254540594752243"+ \
"52584907711670556013604839586446706324415722155397"+ \
"53697817977846174064955149290862569321978468622482"+ \
"83972241375657056057490261407972968652414535100474"+ \
"82166370484403199890008895243450658541227588666881"+ \
"16427171479924442928230863465674813919123162824586"+ \
"17866458359124566529476545682848912883142607690042"+ \
"24219022671055626321111109370544217506941658960408"+ \
"07198403850962455444362981230987879927244284909188"+ \
"84580156166097919133875499200524063689912560717606"+ \
"05886116467109405077541002256983155200055935729725"+ \
"71636269561882670428252483600823257530420752963450"
print(max(reduce(op.mul, map(int, n[i:i + 5]), 1) for i in range(len(n) - 5)))
