%I #15 Feb 14 2021 12:34:25

%S 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,

%T 32,12,35,4,16,22,15,8,40,23,19,10,44,14,47,15,11,28,50,7,10,9,23,18,

%U 56,7,19,12,25,34,62,12,65,35,13,5

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

%H Wilf A. Wilson, <a href="/A290289/b290289.txt">Table of n, a(n) for n = 1..1000</a>

%H James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, <a href="https://arxiv.org/abs/1706.04967">Maximal subsemigroups of finite transformation and partition monoids</a>, arXiv:1706.04967 [math.GR], 2017.

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

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

%Y Cf. A001221, A008472.

%K nonn

%O 1,1

%A _James Mitchell_ and _Wilf A. Wilson_, Jul 26 2017