Partitions into Sum-free Sets

We define a sum as a set {x, y, z} of distinct natural numbers such that x + y = z, and let Nm = {1, 2, . . . , m}. We introduce a new sequence h(n) defined as the smallest s such that there is no partition of Ns into n sum-free parts. We determine h(n) for n = 3, 4 after easily noting that h(1) = 3 and h(2) = 9. We find that h(3) = 24 and h(4) = 67 using a computer program.