When $A_n = n$, the function $f$ defined above counts the number of odd divisors of $n$.

It is conjectured that if $A =\{a_1 < \cdots\}$ and $g$ counts the number of representations $$n=\sum_{u\leq i\leq v}a_i$$ such that the sum has at least two terms, then for all $n$ we have $1 \leq g(n)$ for sufficiently large $n$.