A290289 The number of maximal subsemigroups of the monoid of partial orientation-preserving and reversing injective mappings on the set [1..n].

2, 2, 5, 4, 7, 7, 10, 4, 5, 9, 14, 7, 16, 11, 11, 5, 19, 7, 22, 9, 13, 16, 26, 7, 8, 17, 6, 11, 32, 12, 35, 4, 16, 22, 15, 8, 40, 23, 19, 10, 44, 14, 47, 15, 11, 28, 50, 7, 10, 9, 23, 18, 56, 7, 19, 12, 25, 34, 62, 12, 65, 35, 13, 5

Offset: 1

Author

James Mitchell and Wilf A. Wilson, Jul 26 2017

Keywords

• nonn

Links

• Wilf A. Wilson, Table of n, a(n) for n = 1..1000
• James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.

Crossrefs

Cf. A001221, A008472.

Programs

Mathematica

a[1] = a[2] = 2; a[n_] := PrimeNu[n-1] + DivisorSum[n, Identity, PrimeQ]+1; Array[a, 64] (* Jean-François Alcover, Feb 18 2019 *)

Formula

a(n)= A001221(n -1) + A008472(n) + 1, n > 2.