JavaScript (ES6), 53 bytes
Expects (b)(n). Returns 0 or 1.
b=>g=(n,i=d=1)=>i>b?0:++d>n?1:n%d?g(n,1):g(n/d,i*d--) Arnauld
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Expects (b)(n). Returns 0 or 1.
b=>g=(n,i=d=1)=>i>b?0:++d>n?1:n%d?g(n,1):g(n/d,i*d--)