Power-Smoothness

Definition 1.1 (Power-smooth)   Let $B$ be a positive integer. A positive integer $n$ is $B$-power-smooth if all prime powers dividing $n$ are less than or equal to $B$. The power-smoothness of $n$ is the largest $B$ such that $n$ is $B$-power-smooth.

The following two PARI functions compute whether or not an integer is $B$-power-smooth and also the power-smoothness of $n$.

{ispowersmooth(n, B) =   \\ true if and only if n is B-powersmooth
   local(F,i);
   F = factor(n);
   for(i=1,matsize(F)[1],if(F[i,1]^F[i,2]>B,return(0)));
   return(1);
}

{powersmoothness(n) =    \\ the powersmoothness of n.
   local(F,L,i);
   F = factor(n);
   L = 1;
   for(i=1,matsize(F)[1],L=max(L,F[i,1]^F[i,2]));
   return(L);
}