%I #23 Jan 04 2016 17:54:32
%S 0,0,2,3,2,1,2,2,0,3,2,1,2,6,1,15,2,1,2
%N Number of different quasi-orders with n labeled elements, modulo n.
%C Remainder when number of different quasi-orders with n labeled elements is divided by n.
%C If n is an odd prime, a(n) = 2 because of the fact that A000798(p^k) == k + 1 mod p for all primes p. For k = 1, A000798(p) == 2 mod p for all primes p.
%C Currently, A000798 has values for n <= 18. However, thanks to A000798(p) == 2 mod p, we know that a(19) = 2.
%C How is the distribution of other terms such as 1 and 3 in this sequence?
%H Muhammet Yasir Kizmaz, <a href="http://arxiv.org/abs/1503.08359">On The Number Of Topologies On A Finite Set</a>, arXiv preprint arXiv:1503.08359 [math.NT], 2015.
%F a(A000040(n)) = 2, for n > 1.
%e a(4) = A000798(4) mod 4 = 355 mod 4 = 3.
%e a(5) = A000798(5) mod 5 = 6942 mod 5 = 2.
%e a(6) = A000798(6) mod 6 = 209527 mod 6 = 1.
%Y Cf. A000798.
%K nonn,more
%O 1,3
%A _Altug Alkan_, Dec 21 2015