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

1,5

Links

Table of n, a(n) for n=1..39.

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

Example

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

Crossrefs

Cf. A124506.

Sequence in context: A007359 A213424 A174427 * A364062 A164988 A322391

Adjacent sequences: A158203 A158204 A158205 * A158207 A158208 A158209

Keyword

nonn,more

Author

Steven Finch, Mar 13 2009

Status

approved