def numberofdivisors(n):
if n == 1:
return 1
pf = prime_factorization(n)
lookup = Counter(pf)
numDivisors = 1
for val in lookup.values():
numDivisors *= (val + 1)
return numDivisors
def number_of_divisors(n):
""" Calculate the number of divisors of n.
Every integer n can be written as a product of prime factors e.g.
n = p^a * q^b * r^c
and the number of divisors = (a + 1)(b + 1)(c + 1)...
"""
divisors = 1
prime_factors = prime_factorization(n)
for v in prime_factors.itervalues():
divisors *= (v + 1)
return divisors
def divisors(n):
"""Finds all of the divisors for a given number, including 1 and itself.
Returns a list containing all the divisors for a number"""
if n == 1:
yield 1
return
factors = list(prime_factorization(n))
nfactors = len(factors)
f = [0] * nfactors
while True:
yield reduce(lambda a, b: a*b, [factors[x][0]**f[x] for x in range(nfactors)], 1)
i = 0
while True:
f[i] += 1
if f[i] <= factors[i][1]:
break
f[i] = 0
i += 1
if i >= nfactors:
return
def divisors(n):
"""Finds all of the divisors for a given number, including 1 and itself.
Returns a list containing all the divisors for a number"""
if n == 1:
yield 1
return
factors = list(prime_factorization(n))
nfactors = len(factors)
f = [0] * nfactors
while True:
yield reduce(lambda a, b: a * b,
[factors[x][0]**f[x] for x in range(nfactors)], 1)
i = 0
while True:
f[i] += 1
if f[i] <= factors[i][1]:
break
f[i] = 0
i += 1
if i >= nfactors:
return
"""The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?""" import primes print(primes.prime_factorization(600851475143)[-1])
"""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 positive number that is evenly divisible by all of the numbers from 1 to 20?"""
from collections import defaultdict, Counter
import primes
d = defaultdict(int)
for i in range(2, 21):
pf = primes.prime_factorization(i)
for k, v in Counter(pf).items():
d[k] = max(d[k], v)
lcm = 1
for k, v in d.items():
lcm *= pow(k, v)
print(lcm)