A158206 Number of irreducible numerical semigroups with Frobenius number n; that is, irreducible numerical semigroups for which the largest integer not belonging to them is n.

1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 6, 2, 8, 6, 7, 7, 15, 7, 20, 11, 18, 20, 36, 14, 44, 35, 45, 37, 83, 36, 109, 70, 101, 106, 174, 77, 246, 182, 227

Offset: 1

Author

Steven Finch, Mar 13 2009

Keywords

• nonn
• more

Examples

			a(5)=2: the 2 irreducible semigroups generated by {3, 4} and {2, 7} have Frobenius number 5.
		

Links

• S. R. Finch, Monoids of natural numbers
• S. R. Finch, Monoids of natural numbers, March 17, 2009. [Cached copy, with permission of the author]
• Calvin Leng, Christopher O'Neill, A sequence of quasipolynomials arising from random numerical semigroups, arXiv:1809.09915 [math.CO], 2018.
• J. C. Rosales, P. A. Garcia-Sanchez, J. I. Garcia-Garcia and J. A. Jimenez-Madrid, Fundamental gaps in numerical semigroups, Journal of Pure and Applied Algebra 189 (2004) 301-313.
• Clayton Cristiano Silva, Irreducible Numerical Semigroups, University of Campinas, São Paulo, Brazil (2019).
• Eric Weisstein's World of Mathematics, Frobenius number
• Index entries for sequences related to semigroups

Crossrefs

Cf. A124506.