Check B-powersmoothness
J, 14 13 bytes
&lt;[:&gt;./2^/@p:]

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-1 byte thanks to @Jonah
A dyadic function. The right argument is \$n\$, the left argument is \$B\$. Returns 0 if \$n\$ is \$B\$-powersmooth, 1 otherwise.
How it works
&lt;[:&gt;./2^/@p:]  NB. left arg = B, right arg = n
      2   p:]  NB. Prime factorization of n,
               NB. given as a 2-row matrix of [primes, exponents]
       ^/@     NB. Evaluate all pi^ei for each prime factor
 [:&gt;./         NB. Maximum of all prime powers found above
&lt;              NB. 1 if the above is greater than B, 0 otherwise