Squarefree Palindromes
Python 2, 82 75 bytes
n=0
while 1:
 n+=1
 if`n`[::-1]==`n`*all(n%i**2for i in range(2,n)):print n

Try it Online!
If this was a decision problem (54 bytes):
lambda n:`n`[::-1]==`n`*all(n%i**2for i in range(2,n))

Explanation:
`n`[::-1]==`n`                     # If n is a palindrome. `n` is repr(n).
                                   # We check that it's the same
                                   # backwards and forwards.
              *                    # Multiplplying 2 booleans is AND
all(n%i**2for i in range(2,n))     # Check that squares of all #'s &lt; n do not divide n