Numerical semigroups counted by maximum primitive are Möbius transforms of those counted by Frobenius number, and almost all with large enough maximum primitive satisfy Wilf's conjecture.
Numerical semigroups with large embedding dimension satisfy Wilf’s conjecture
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On counting numerical semigroups by maximum primitive and Wilf's conjecture
Numerical semigroups counted by maximum primitive are Möbius transforms of those counted by Frobenius number, and almost all with large enough maximum primitive satisfy Wilf's conjecture.