Hi,
Generating a long list takes time. If speed is an issue too, you could consider defining your own squarefree test.
sage: %cython
sage: cimport cython
sage: @cython.cdivision(True)
sage: #Fast up to 5*10^8
sage: cpdef bint is_csquarefree(long long n, unsigned long long priem=10**6):
... cdef unsigned long p
... cdef unsigned int* eerste=[2,3,5]
... cdef unsigned int i=1,k
... cdef unsigned int* diff=[6,4,2,4,2,4,6,2]
... if not n: return 0
... if n<0: n=-n
... for k in xrange(3):
... if not n%eerste[k]:
... n//=eerste[k] #In 539 of 900 cases a number not dividable by 4,9,25
... if not n%eerste[k]: return False
...
... p=7
... while p<=priem and p*p<=n:
... if not n%p:
... e=1 ; n//=p
... if not n%p: return False
...
... p+=diff[i%8]
... if not p%7: i+=1 ; p+=diff[i%8] #Small lost of time
... i+=1
... return True
Test it:
sage: for k in xsrange(1,1000):
... if is_csquarefree(k)!=is_squarefree(k): print k
Enjoy speed:
sage: timeit('for k in xrange(10^8,10^8+10^3): is_squarefree(k)==True')
sage: timeit('for k in xrange(10^8,10^8+10^3): is_csquarefree(k)==True')
25 loops, best of 3: 29.2 ms per loop
125 loops, best of 3: 4.86 ms per loop