def is_squarefree(n):
if n == 1:
return True
quotient = n
count = 1
while count == 1:
prime, _ = first_prime_divisor(quotient)
quotient, count = robust_divide(quotient, prime, include_count=True)
if quotient == 1:
return (count == 1)
return False
def all_radicals(n):
PRIMES = sieve(n)
result = {1: 1}
for i in range(2, n + 1):
if i in PRIMES:
result[i] = i
prime, quotient = first_prime_divisor(i, PRIMES)
if quotient % prime == 0:
result[i] = result[quotient]
else:
result[i] = result[quotient]*prime
return result
