Erdős Problem 845

Reference: erdosproblems.com/845

theorem erdos_845 (C : ℝ) (hC : 0 < C) : let f := fun (x : ℕ × ℕ) => match x with | (k, l) => 2 ^ k * 3 ^ l; {x : ℕ | ∃ (B : Finset (ℕ × ℕ)) (h : B.Nonempty) (_ : ↑(B.sup f) ≤ C * ↑(B.inf' h f)), ∑ x ∈ B, f x = x}.HasDensity 0 ↔ sorry

Let $C > 0$. Is it true that the set of integers of the form $n = b_1 + \cdots + b_t$, with $b_1 < \cdots < b_t$, where $b_i = 2^{k_i}3^{l_i}$ for $1 \leq i\leq t$ and $b_t \leq Cb_1$ has density $0$?