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from operator import itemgetter
from common import sieve
limit = 100000
primes = sieve(limit).primes()
prime_list = list(primes)
prime_list.sort()
def rad(n):
result = 1
if n in primes:
return n
for p in prime_list:
if result*p > n:
break
if n % p == 0:
result *= p
return result
radlist = []
for n in xrange(1, limit+1):
radlist.append((n, rad(n)))
radlist.sort(key=itemgetter(1))
print radlist[10000-1][0]
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