  George Andrews recently proved a new identity between the cardinalities of
the set of Semi-Fibonacci partitions and the set of partitions into powers of
two with all parts appearing an odd number of times. This paper extends the
identity to the set of Semi-$m$-Fibonacci partitions of $n$ and the set of
partitions of $n$ into powers of $m$ in which all parts appear with
multiplicity not divisible by $m$.
