Numerical semigroups in a problem about economic incentives for consumers

Motivated by a promotion to increase the number of musical downloads, we introduce the concept of C-incentive and show an algorithm that compute the smallest C-incentive containing a subset X ⊆ N. On the other hand, in order to study C-incentives, we see that we can focus on numerical C-incentives. Then, we establish that the set formed by all numerical C-incentives is a Frobenius pseudo-variety and we show an algorithmic process to recurrently build such a pseudo-variety.