A079171 - OEIS

%I #8 Aug 03 2025 17:08:57

%S 1,4,6,3,12,78,3237,2,1,14,30,275,495,48810,178932325

%N Number of isomorphism classes of closed binary operations (groupoids) on a set of order n, listed by class size.

%C Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

%C A002489(n) is equal to the sum of the products of each element in row n of this sequence and the corresponding element of A079210.

%C The sum of each row n is given by A001329(n).

%H C. van den Bosch, <a href="http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>

%e First four rows:

%e   1;

%e   4, 6;

%e   3, 12, 78, 3237;

%e   2, 1, 14, 30, 275, 495, 48810, 178932325.

%Y Cf. A002489, A001329. a(n, A027423(n)) = A030245(n).

%K nonn,tabf

%O 1,2

%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003