A number is said to be biquadratefree (or quarticfree) if its prime factorization contains no quadrupled factors. All primes
and prime powers 
with 
are therefore trivially biquadratefree. The biquadratefree
numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, ... (OEIS A046100).
The biquadrateful numbers (i.e., those that contain at least one biquadrate) are
16, 32, 48, 64, 80, 81, 96, ... (OEIS A046101).
The number of biquadratefree numbers less than 10, 100, 1000, ... are 10, 93, 925,
9240, 92395, 923939, ..., and their asymptotic density is 
, where 
is the Riemann zeta
function.
