A number n is called amenable if it can be built up from integers a_1, a_2, ..., a_k by either addition or multiplication such that sum_(i = 1)^n a_i = product_(i = 1)^n a_i = n (Tamvakis 1995). The solutions are the numbers n such that n congruent 0 or 1 (mod 4), excluding n = 4, giving 1, 5, 8, 9, 12, 13, 16, 17, ... (OEIS A100832). For example, 5 and 8 are amenable since 5 | = | 1 - 1 + 1 - 1 + 5 | = | 1×(-1)×1×(-1)×5 8 | = | 1 - 1 + 1 - 1 + 1 + 1 + 2 + 4 | = | 1×(-1)×1×(-1)×1×1×2×4.

amenable | composite number | partition | sum