cp's OEIS Frontend

A079175 Number of isomorphism classes of associative closed binary operations (semigroups) on a set of order n, listed by class size.

%I A079175 #15 Jan 26 2022 17:57:11
%S A079175 1,1,2,3,2,0,7,15,2,0,0,7,5,0,62,112,2,0,0,0,6,0,0,8,0,2,51,0,47,2,
%T A079175 576,1221,2,0,0,0,0,6,0,0,0,0,8,0,0,4,0,48,0,0,0,0,92,0,0,42,506,0,
%U A079175 813,32,7397,19684,2,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,8
%N A079175 Number of isomorphism classes of associative closed binary operations (semigroups) on a set of order n, listed by class size.
%C A079175 Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
%H A079175 Andrew Howroyd, <a href="/A079175/b079175.txt">Table of n, a(n) for n = 0..217</a> (rows 0..8; row 8 was derived from data given in the Distler-Kelsey reference)
%H A079175 C. van den Bosch, <a href="https://web.archive.org/web/20071014230143/http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>
%H A079175 A. Distler and T. Kelsey, <a href="http://arxiv.org/abs/1301.6023">The semigroups of order 9 and their automorphism groups</a>, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
%H A079175 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%F A079175 A079174(n,k) + T(n,k) = A079171(n,k).
%F A079175 T(n, A027423(n)) = A058104(n).
%F A079175 A023814(n) = Sum_{k>=1} T(n,k)*A079210(n,k).
%e A079175 Triangle T(n,k) begins:
%e A079175   1;
%e A079175   1;
%e A079175   2, 3;
%e A079175   2, 0, 7, 15;
%e A079175   2, 0, 0, 7, 5, 0, 62, 112;
%e A079175   2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221;
%e A079175   ...
%Y A079175 Row sums give A027851.
%Y A079175 Cf. A023814, A027423 (row lengths), A079171, A079174, A079210.
%K A079175 nonn,tabf
%O A079175 0,3
%A A079175 Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
%E A079175 a(0)=1 prepended and terms a(16) and beyond from _Andrew Howroyd_, Jan 26 2022