def solve(n):
"""
Count the maximal number of occurrences of every prime number
that appears in the decomposition of each number
until n
"""
p = PrimeDecomposition()
decompositions = dict()
for i in range(2, n + 1):
decompositions[i] = p.decompose(i, [], 0)
multiplicities = dict()
for _, dec in decompositions.iteritems():
primes_occurrences = occurrences(dec)
for prime, prime_occurrences in primes_occurrences.iteritems():
if prime in multiplicities:
multiplicities[prime] = max(
multiplicities[prime],
prime_occurrences
)
else:
multiplicities[prime] = prime_occurrences
solution = 1
for prime, multiplicity in multiplicities.iteritems():
solution *= pow(prime, multiplicity)
return solution
def solve(n=10001):
assert n >= 1
p = PrimeDecomposition()
for i in range(n+10):
p.get_one_more_prime()
return p.primes_list[n - 1]
def sum_prime(n):
p = PrimeDecomposition()
p.get_primes_until(n + 10)
return sum(
[p for p in p.primes_list if p <= n]
)
