Given a positive integer $N$, let $f(N)$ be the number of ways $N$ can be decomposed as a sum of terms of the form $2^i3^j$, where each such term appears at most once in the sum. For example, $f(10) = 5$, since 10 can be expressed as $3^2 + 1, 2^2 + 2 \cdot 3, 2^2 + 3 + 2 + 1, 2 \cdot 3 + 3 + 1,$ and $2^3 + 2$. I would like upper and lower bounds on $f(N)$ in terms of $N$. I am also interested in the more general problem where we look for decompositions as sums of terms of the form $\Pi p_i^{e_i}$ where $\{p_i\}$ are specified primes.