Abstract
A numerical semigroup is irreducible if it cannot be obtained as an intersection of two numerical semigroups containing it properly. If we only consider numerical semigroups with the same Frobenius number, that concept is generalized to atomic numerical semigroup. Based on a previous one developed to obtain all irreducible numerical semigroups with a fixed Frobenius number, we present an algorithm for computing all atomic numerical semigroups with a fixed Frobenius number.
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